Does the dynamic time consistency model of inflation explain cross-country differences in inflation dynamics?

Transcription

1 Does the dynamic time consistency model of inflation explain cross-country differences in inflation dynamics? John F. Boschen School of Business Administration The College of William and Mary P.O. Box 8795 Williamsburg VA 3187 and Charles L. Weise * Department of Economics Gettysburg College Gettysburg, PA 1735 June 001 Revised March 00 Revised June 00 Abstract: Dynamic time consistency models of monetary policy imply that the size of the inflationary response to price shocks and the persistence of inflation is inversely related to factors that enhance the central bank s ability to commit to low average inflation. Hence these models predict that the dynamics of inflation vary over time and across countries in response to changes in measures of political support for low inflation. We find support for this hypothesis in data from eighteen OECD countries over the period However, political variables account for only a small fraction of the variation in inflation dynamics across countries. JEL classification: E31, E4, E58 Key words: central bank, inflation, monetary policy, time consistency * Corresponding author. Telephone: Fax: cweise@gettysburg.edu.

2 1. Introduction The KPBG (Kydland and Prescott 1977, Barro and Gordon 1983) time consistency model of monetary policy has generated an important empirical literature that tests whether political factors that affect the central bank s ability to commit to low inflation are correlated with average inflation rates across countries. While retaining the implications for cross country differences in average inflation, dynamic versions of the KPBG model such as Svensson (1997) and Clark et al. (1999) also pose testable hypotheses about differences in inflation persistence and the response of inflation to price shocks (hereafter referred to as the dynamics of inflation) across countries and over time. The empirical implications of these models have until now received little attention. This paper seeks to fill this gap. Dynamic versions of the KPBG model feature an optimizing central bank operating in an environment in which monetary policy actions taken today alter the bank s choice set in the future. The models typically incorporate rational expectations and imply an inflationary bias arising from the bank s inability to commit to the optimal monetary policy. An early example is Ball (1995), in which one-time price (aggregate supply) shocks trigger persistent periods of inflation due to the response of weak policymakers. 1 Svensson (1997) allows for a continuum of weak or strong monetary policymakers indexed by the relative penalty weight on employment versus inflation stabilization in the central bank s loss function. In the presence of price shocks and a source of persistence (here, persistence in the level of employment), the dynamics of inflation are affected by the strength or weakness of the central bank. Specifically, a weak policymaker (i.e. one with a high penalty weight on employment deviations) allows more of a 1 Earlier papers which apply the insights of the KPBG model to dynamic settings, but which are less closely linked to the present paper, include Backus and Driffil (1985), Barro (1986), and Cukierman (1986). The argument that a country s inflation dynamics are affected by the degree to which the monetary authority is perceived to be

3 given price shock to be transmitted into inflation and less into real activity. Clark et al. (1999) provides a formal linkage between inflation persistence (the dependence of current inflation on past values of inflation) and the penalty weight on inflation in the central bank s loss function. In that model, the weak policymaker allows both a greater inflationary response to price shocks and a greater degree of inflation persistence. In testing the empirical implications of the static KPBG model, researchers have identified political and institutional factors likely to be associated with weight conservativeness such as central bank independence, political stability, and the conservative leanings of the elected government. The question is then asked whether variation in these factors can account for differences in average inflation rates across countries (see Campillo and Miron, 1997, for an excellent survey of this literature). The present paper exploits the same political and institutional variables to test the implications of dynamic KPBG models: specifically, that countries with weak central banks tend to experience a larger inflationary response to price shocks and a higher degree of inflation persistence than those with more weight conservative central banks. We ask whether variation in these political and institutional variables can account for differences in inflation dynamics across countries. In fact, cross-country differences in inflation dynamics are substantial. In Table 1 we report regressions of CPI inflation on lagged inflation and changes in oil and commodity prices for eighteen OECD countries for the period Two facts are apparent from these regressions. First, there is considerable variation in the estimated response of inflation to price shocks. For example, the response of inflation to a ten percentage point increase in oil prices varies committed to low inflation goes back at least to Sargent s (198) persuasive case studies showing that inflation persistence is related to the nature of the monetary and fiscal policy regime. A recent paper that tests the empirical implications of the dynamic time consistency model is Ireland (1999). His study is confined to the U.S. and does not consider the role of institutional variables.

4 from essentially zero in the United States and New Zealand to 0.47 percentage points in Sweden. The response of inflation to a ten percentage point increase in commodity prices varies from zero in New Zealand to 1.5 percentage points in Japan. Second, there is also wide variation in the degree of inflation persistence measured by the coefficient on lagged inflation: the coefficient ranges from 0.48 in Norway and Switzerland (implying a half-life of 0.9 years) to 0.93 in Canada (a half-life of 9.7 years). Figure 1, which plots CPI inflation in the G-7 countries relative to 197 levels, shows the variation in inflation dynamics following the price shocks of the early 1970 s. In Germany the price shocks had a very small short-term effect on inflation and by 1975 the inflation rate had returned to the 197 level. In Italy and the United Kingdom, by contrast, inflation peaked at 11.8 and 14.9 percentage points above the 197 level respectively, and remained at elevated levels through The differences in inflation performance among these countries is consistent with the strong estimated response of inflation to oil and commodity price shocks in Italy and the United Kingdom and the relatively weak estimated response in Germany. In this paper we use data from 18 moderate inflation OECD countries over the period to test the implications of the dynamic KPBG model. We have two objectives: to test whether political and institutional variables are associated with differences in the responsiveness of inflation to price shocks and in the degree of inflation persistence, and to see how much of the cross-country variation in inflation dynamics can be explained by the model. As emphasized recently by Brumm (000), the empirical tests of the kind pursued here are joint tests of the hypotheses that the model s predictions are true and that the data used to indicate a weak or strong inflation policy regime actually measure the regime accurately. Our empirical work draws on some of the standard measures of policymaker type but we recognize that a single measure of the political environment probably will not fully capture a central bank s stance on inflation. Thus, as part of our analysis, we 3 The regression model used in Table 1 is a version of the empirical model, equation (11), that we develop below. 3

5 construct an index of the central bank s weakness in inflation control based on the Hauser and Goldberger (1971) multiple-indicator multiple-cause (MIMC) framework. We proceed as follows. Section presents two models of inflation, static and dynamic, to motivate the empirical analysis. Section 3 describes the methodology and the data used in the empirical study. Section 4 presents the main empirical results. In Section 5 we verify that these results are robust to a number of changes in the sample and in model specification. Section 6 concludes.. Inflation and the political environment First we present a simple static model in which a central bank chooses the optimal degree of inflation in response to a shock to the unemployment rate. In this model the key variable affecting the inflationary response to these shocks is the weight on unemployment in the central bank s loss function. We then extend this model along the lines of Clark et al. (1999) to show that in a dynamic setting the degree of inflation persistence is also affected by the penalty weight on unemployment. In the static model the Phillips curve is u = u α( π π ) + S (1) t n t e t t where u t is the actual unemployment rate, u n is the natural rate of unemployment, π t is the inflation rate, π e t is the expected inflation rate, and S t is a mean-zero shock to unemployment. Agents in the economy have rational expectations and set π e t prior to the realization of the unemployment shock. The central bank sets the inflation rate after having observed the value of S t. The central bank chooses the inflation rate to minimize its loss function, given by t 1 L( π, u ) = [( π π*) + λu ] () t t t where π* is the target rate of inflation. The parameter λ measures the weakness of the central bank with regard to controlling inflation. When λ=0 the central bank is a strict inflation fighter. 4

6 The larger is λ, the more importance the central bank attaches to stabilizing unemployment rather than the inflation rate. We interpret λ as a function of the political environment within which the central bank operates. That is, left-wing governments or those with a precarious hold on power may impose a high penalty weight on unemployment on the central bank. A central bank with strong legal independence, on the other hand, may be able to resist these pressures. The effect of λ is therefore the focus of our empirical work. The central bank s optimal choice of inflation is easily computed in this simple framework. Minimizing () with respect to (1) yields π t = π* + αλu t. Under rational expectations, π e t = π* + αλu n. Combining these equations we get the optimal inflation rule αλ π t = π * +αλun + S t. (3) 1+ α λ The central bank sets the inflation rate higher than the target rate on average as in the KPBG model. The weaker is the central bank (the larger the weight on unemployment), the higher is the average rate of inflation. For present purposes, the most important implication of the model is that large values of λ cause inflation to increase more in response to an adverse shock. An adverse shock to unemployment forces the central bank to choose some combination of higher inflation and unemployment, and the optimal combination is a function of the weight on unemployment in the central bank s loss function. This static model is extended to incorporate inflation persistence using a modified version of the model in Clark et al. (1999). 4 The key feature of the dynamic model is that the Phillips curve now has forward and backward-looking components. The forward-looking part is a rational expectations inflation forecast error, π t E t-1 π t = π t π e t. The backward-looking 4 Svensson (1997) has also extended the static model to incorporate persistence in the level of employment. One can easily verify that in his model as well, the response of inflation to supply shocks is larger for weaker central banks. 5

7 component, π t -π t-1, is usually associated with wage or price inertia in an overlapping contracts framework as in Fischer (1977), Taylor (1980) and Fuhrer and Moore (1995). The present model differs from the Clark model in that we assume that the central bank controls inflation directly, rather than through the interest rate, and we allow for the average inflation bias described by Barro and Gordon (1983). The Phillips curve for this economy is: u ) + (1 θ)( π π )] + S t = u n α[ θ( π t π t 1 t e t t (4) The model in equation (4) satisfies what Clark et al. refer to as the weak form of the natural rate hypothesis since according to equation (4), the unemployment rate can rest permanently below the natural rate only if the inflation rate continually accelerates. 5 Because of the persistence of inflation, the central bank must consider the implications of its current-period actions for inflation and unemployment in the future by solving the infinite horizon problem min V { πs } t 1 = E t 1 s= t β s t L( π,u s s ) (5) subject to () and (4), where β, 0<β<1, is the central bank s discount factor. The solution to this model is similar to the one given by Clark et al. The central bank solves the dynamic programming problem t 1 V( π ) = E min{ [( π π*) + λu ] + βv( π )} (6) t 1 t 1 πt t subject to (4). Because of the linear-quadratic form of the problem, the value function will be t quadratic; let V( π ) = γ 0 + γ π γ π. The solution to this model is the reaction function for inflation 5 More precisely, the model is consistent with long-run neutrality, in the sense of Fisher and Seater (1993), with regard to a permanent change in the price level and with long-run neutrality with regard to a permanent increase in the level of inflation, but exhibits long-run nonneutrality with regard to a permanent acceleration in inflation. 6

8 π t = a + bs t + cπ t-1 (7) where π* βγ1 + αλu n a = (8a) 1+ βγ + α λθ αλ b = (8b) 1+ βγ + α λ α λθ c = (8c) 1+ βγ + α λθ We solve for γ 1 and γ by substituting equations (8a-c) into (6) and matching coefficients. This gives ( a π*)c + αλθ(u n αθa)(1 c) + βacγ γ 1 = (9a) 1 βc c + λ( αθ) (1 c) γ = (9b) 1 βc To solve for c, we combine (8c) and (9b) to form the cubic expression c = α λθ(1-c)[1-βc -βθ(1-c)c] (10) We prove in Appendix A that for all α>0, λ>0, θ (0,1) and β (0,1) there exists a unique stable solution c (0,1) to equation (10). There are two unstable solutions as well, but it is the stable solution that is relevant for our purposes. Once the solution to equation (10) is found we can derive an expression for γ from equation (9b) and use this to solve for b in equation (8b). The value for a can be found by combining equations (8a) and (9a). One key implication of this model involves the effect of λ on c, the parameter which measures the persistence of inflation. Appendix A includes a proof that a high value of λ (implying a weak central bank) produces a high degree of inflation persistence. After a price 7

9 shock has caused inflation to rise, a strong central bank will bring inflation down quickly towards its target, while a weak central bank will be unwilling to pay the unemployment cost of such an action. Consequently, the inflation rate will remain above target for a longer time under a weak central bank. The effect of λ on the average rate of inflation (a) and the response to price shocks (b) can be computed, but it is difficult to sign the derivatives in these cases. But numerical simulations (available from the authors) indicate that a higher value of λ also causes average inflation to be higher and the inflationary response to price shocks to be stronger for a wide range of parameter values. Thus the main results from the static model hold in a dynamic setting as well. 3. Data and empirical framework The solution for inflation, equation (7), suggests a linear empirical framework for inflation in both shocks and inflation persistence. However, as shown in section, the relation between the penalty weight parameter, λ, and the coefficient values is complicated and nonlinear. In the empirical work, we assume a linear relationship between the coefficient values and λ. In addition to giving us the empirical tractability needed in a multi-country study, this assumption captures the essential testable implications of the models in section ; the stronger the commitment to low inflation (i.e. the smaller is λ), the smaller is the inflation response to shocks and the less persistent is inflation. The empirical model is of the form INF it = A 0it + A 1 DUR it-1 + B 0it DOIL t-1 + B 1it DCOM t-1 + C it INF it-1 + ε it (11) where A 0it = a 0 + a 1 Z it, B 0it = b 0 + b 1 Z it, B 1it = b + b 3 Z it and C it = c 0 + c 1 Z it. The dependent variable, INF it, is the annual CPI inflation rate in country i in year t. The two variables used as price shocks are the lagged change in the dollar price of oil, DOIL t-1, and 8

10 an index of world non-fuel primary commodity prices, DCOM t-1. 6 Lagged inflation is included to measure inflation persistence. We also add to the empirical model the change in the unemployment rate, DUR t-1. We do this for two reasons. The link between inflation and real activity is well documented in the empirical Phillips curve literature (Stock and Watson, 1999, among others). In addition, Faust and Irons (1999) argue that including a real variable in the inflation equation is a partial corrective to the potential problem of endogenous political variables. 7 The variable Z it represents political variables that could affect the weight conservativeness of the central bank. The central feature of the empirical model is that the coefficients describing the inflation dynamics of concern in this paper, B 0it, B 1it, and C it, are functions of the Z it variables. 8 The model can be thought of as a restricted version of a more general model in which inflation responses and persistence are allowed to vary arbitrarily across countries. Here, variation in inflation dynamics is restricted to arise solely from variation in policymaker type as measured by political variables. We use four different measures for Z. The first three are Cukierman s (199) index of central bank independence (CBI), the frequency of changes in government (FREQ), representing political instability, and Alesina and Roubini s (1997) measure of the ideological orientation of the ruling party in government (ORIENT). Each of these variables is intended to serve as a proxy 6 The effect of oil and commodity prices on inflation in OECD countries has been examined in several papers, including Bernanke, Gertler, and Watson (1997), Boughton and Branson (1991) and Bruno and Sachs (1985). We use a specification with lagged values of DOIL and DCOM because early experiments showed only the lagged value of DCOM had statistical significance. 7 The omission of an exchange rate from equation 11 reflects the assumption that the exchange rate affects inflation only through its impact on unemployment. Alternatively, the exchange rate could have a direct supply-side effect on inflation analogous to that of oil and commodity prices. We chose not to make this assumption because whereas a strong case can be made that oil and commodity prices represent exogenous shocks, the exchange rate is likely to be strongly influenced by the inflation rate. The endogeneity of the exchange rate would result in biased coefficient estimates. 9

11 for the strength or weakness of the central bank s commitment to low inflation. When an adverse price shock occurs, an independent central bank is more likely to resist pressures to inflate than one that is tied to the government in power. Policymakers in countries that have experienced frequent turnover in government may be reluctant to sacrifice employment stability in order to stabilize inflation. Likewise left-wing governments, whose electoral base includes labor unions and others for whom unemployment is the major economic concern, are less likely than rightwing governments to act decisively against inflation. Because it is unlikely that a single measure of the political environment completely describes the central bank s stance on inflation, we construct an index of the central bank s weakness toward controlling inflation. We combine the political variables by applying the Hauser and Goldberger (1971) multiple-indicator multiple-cause (MIMC) method to decade averages of the data. 9 Central bank weakness toward inflation, denoted WEAK, is related to the political variables by WEAK = Zµ + η. (1) Z includes decade dummies in addition to CBI, FREQ, and ORIENT. µ is a parameter vector and η has mean zero and finite variance. Weakness is unobservable, but affects an indicator variable according to Π = Π 0 + φweak + ε (13) where Π 0 and φ are parameters. The random variable ε has mean zero and finite variance and is uncorrelated with η. Our indicator variable is decade average inflation. Including WEAK as an explanatory variable in our regressions amounts to imposing the restriction that the political 8 The effect of weakness on the inflationary response to changes in unemployment is not clear-cut, so we restrict the coefficient on DUR it-1 to be constant across countries and time. None of our results are altered if we allow the coefficient on DUR it-1 to be affected by our political variables. 10

12 variables affect the dynamics of inflation only to the extent that they also affect long-run average inflation rates. We provide tests of this restriction below. Estimates of φ and µ are extracted using a modified GLS procedure on the coefficient estimates from the reduced form regression Π = Π 0 + ZP + u. (14) Equation (14) is estimated by OLS on pooled decade averages of the data for the eighteen countries in our sample. 10 The estimated reduced form regression is INF = -.7(4.5) D 1960s +.7(0.54) D 1970 s (3.4) CBI +.05(1.80) FREQ - 0.5(1.61) ORIENT (t statistics in parentheses). From this equation we derive φ=15.36 and WEAK = D 1960s D 1970 s 0.9 CBI FREQ 0.03 ORIENT. A time series of weakness for each country is computed by applying the estimated values of µ to annual data Empirical results We use annual data from eighteen OECD countries for the period The data is pooled and the model is estimated as a seemingly unrelated regressions (SUR) model to control for possible contemporaneous cross-country correlation in the residuals. Results of the 9 See Avery (1979) and Bernanke and Blinder (199) for applications of this technique to measuring the stance of monetary policy. 10 We include decade dummies to represent unobserved factors that may have had a common effect on countries attitudes toward inflation. An example would be innovations in economic theory during the 1970 s, specifically the falling out of favor of Keynesian economics and the rise of monetarism and rational expectations. De Long (1997) points to these intellectual developments as a primary cause of both the rise of inflation in the U.S. in the 1970 s and its subsequent decline in the 1980 s. 11 While the Hauser-Goldberger procedure normalizes WEAK so that its standard deviation equals one, our annual weakness series (as opposed to the series of decade averages) are not guaranteed to have this property, nor are the means guaranteed to equal zero, as can be seen in Appendix Table B1. The WEAK variable is a construct variable and like the other indicators of political stance, is not likely to measure this concept without error. As pointed out by Pagan (1984) this uncertainty in measurement implies that the standard error of the inflation regressions may be understated. 1 The countries in our data set are very similar to those in the high-income sample used by Campillo and Miron and others. Both data sets include Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Italy, Japan, the Netherlands, New Zealand, Norway, Sweden, Switzerland, UK and USA. Our data set includes Spain, but excludes Iceland and Luxembourg (included in Campillo and Miron) because of data availability. The sample ends in 1994 because some of the political variables are not available past this date. 11

13 estimation of equation (11) are presented in Table. Each column of the table reports the results from regressions using a single political variable. The first column of figures in Table reports coefficient estimates and t statistics for the regression in which CBI interacts with the shocks, DOIL(-1), DCOM(-1), and with lagged inflation; FREQ is interacted in column, and so on. Before discussing the main results in Table, two less central findings should be noted. First, the coefficients on lagged inflation, unemployment, oil prices and commodity prices are strongly significant and quite stable across regressions. Second, the effects of the political variables on the level of inflation are consistent with theory and statistically significant at the five percent level or better. To calculate the level effect of the political variables it is necessary to evaluate the interaction terms at the overall mean values of DOIL(-1), DCOM(-1) and INF(- 1). Making this calculation, we find that the estimated effect of CBI, FREQ, ORIENT, and WEAK (with t statistics in parentheses) are 1.4 (3.88), 0.48 (.43), -0.0 (4.97), and 3.49 (5.96) respectively. Thus central bank independence and right wing governments lower inflation on average while political instability and weakness raise inflation on average. The effect of political instability is consistent with Campillo and Miron s (1997) findings. We find a statistically significant effect of central bank independence, in contrast to Campillo and Miron. Higher average inflation under left-oriented governments is consistent with findings by Alesina and Roubini (1997). The key results concern the coefficients on the interaction terms. The model in the first column suggests that the more independent the central bank, the less inflation rises in response to an oil or commodity price shock, and the less persistent is inflation. Two of the coefficients are statistically significant at the five percent level or better, but the coefficient on the interaction of 1

14 CBI and DOIL is not. A joint test of the significance of the interaction terms rejects the hypothesis that they are zero at the one percent level. In the regression in the second column, in which FREQ is used as the political variable, the coefficients on the interaction terms are all positive. This implies that less stable governments accommodate shocks more and allow inflation to be more persistent. The coefficient on the interaction with lagged inflation, however, is not statistically significant. The F test rejects the joint hypothesis that all the interaction terms are zero at the one percent level. The political orientation of the ruling party has a more ambiguous effect on the dynamics of inflation. As shown in the third column of Table, inflation persistence is estimated to be smaller under conservative governments and the estimated response of inflation to oil price shocks is smaller. However, these effects are not statistically significant. On the other hand, we find a small positive effect of political orientation on the response to commodity price shocks, which is not consistent with theory. The comparative weakness of these results may be in part a measurement problem. ORIENT judges the orientation of a political party relative to other parties in the same country and not to parties in other countries. Therefore it does not make a distinction between the orientation of, for example, the U.S. Democratic Party versus the French Socialist Party. The weakness index provides the strongest evidence in support of the model. Each of the interaction terms in Table is positive, implying that weaker policymakers accommodate shocks more and allow inflation to persist longer. Each of the coefficients is significant at the five percent significance level or lower and the hypothesis that all coefficients are zero is rejected at the one percent significance level. 13

15 As previously noted, the model imposes the restriction that the political variables affect inflation dynamics through the same channel that they affect long-run average inflation. If this restriction holds, the political variables should not exert an independent effect on inflation dynamics once weakness is accounted for. Table 3 shows that this restriction is for the most part supported by the data. In columns one to three each of the political variables is added in turn to the weakness regression in Table. The coefficients on the interaction terms between weakness and the economic variables retain their positive signs and statistical significance in all regressions. In only two cases are the coefficients on the interaction terms involving political variables significant, implying rejection of the restriction. The coefficient on the interaction between oil prices and FREQ has the expected sign and is significant, but in this case the joint hypothesis that all the coefficients on the interaction terms involving political variables are zero is not rejected at the ten percent level. The coefficient on the interaction between commodity prices and ORIENT is significant (and the joint hypothesis is rejected as well) but the coefficient has the wrong sign. Table 4 illustrates the magnitude of the interaction effects found in Table. Panel A reports the dynamic response of inflation to a permanent doubling of oil prices over a four year horizon. 13 Panel B shows the estimated effect of a doubling of commodity prices. The dynamic responses depend on the values of the political variables. For illustrative purposes, we compute the responses using the average values of CBI, FREQ, and WEAK for Germany and Italy. The choice of these countries is motivated by the fact that they are large economies that, according to our weakness index, are among the strongest and weakest respectively. We also compare the responses for right leaning and left leaning governments by setting ORIENT equal to 1 and 1 14

16 respectively. In each panel of Table 4, the first two columns of figures are computed using coefficient estimates from the first column of Table, the third and fourth columns of Table 4 are computed using coefficient estimates from the second column of Table, and so on. Consider the case of our weakness measure (the last two columns in each panel). Panel A shows that a doubling of oil prices raises inflation in both Germany and Italy, but after one year inflation rises by 1.5 percentage points more in Italy, the weaker country. Inflation then decays at a slower rate in Italy, so that after four years the rise in inflation is almost five times larger in Italy. Over the four year period following the shock, Italy s price level has risen by 6. percentage points while Germany s has risen by 1.7 percentage points. The effect of weakness is stronger when there is a doubling of commodity prices, as shown in Panel B. In this case, inflation rises by almost four percentage points more in Italy in the period after the shock, and the rise in inflation is still over four times as great in Italy four years after the shock. The cumulative effect on the price level is over three times as large in Italy (17.1 percent) as in Germany (5.4 percent). The effects of central bank independence and political instability are smaller but still noticeable. After four years a doubling of oil prices raises the price level by 3.3 percentage points in Italy versus.1 percentage points in Germany when CBI is the conditioning variable and by 9.5 percentage points in Italy versus 4.8 percentage points in Germany when FREQ is used. A doubling of commodity prices raises the price level by 3.3 percentage points in Italy versus 10.4 percentage points in Germany when CBI is the conditioning variable, and percentage points in Italy versus 17.8 percentage points in Germany when FREQ is used. Not surprisingly given the results in Table, the simulations involving political orientation tell a 13 The dynamic response of inflation to a doubling of oil prices is the change in the expected value of inflation in period k brought about by a unit increase in DOIL in period 0 (mathematically, E 0 π k / DOIL 0 ), conditional on the estimated model in Table and assumed values for the political variables, for k=1 to 4. 15

17 conflicting story: while left wing governments inflate more in response to oil price shocks they inflate less in response to commodity price shocks. While it is clear that the indicator variables are significantly correlated with cross-country differences in inflation dynamics, the models fail to account for the range of cross-country variation in dynamics observed in Table 1. Table 5 provides a summary comparison of the coefficients on lagged inflation, DOIL and DCOM from Table 1 with simulated values of the same coefficients from Table. The simulated coefficients were calculated by substituting the mean value of WEAK for each country into the estimated Table, column 4 equation. Each column in the top panel of Table 5 gives the mean, range and standard deviation of the Table 1 coefficients while the middle panel of the table lists the same information for the simulated coefficients. Note that in each case the cross-country means of the simulated coefficients are quite close to the Table 1 mean values. However, the simulated coefficients do not replicate the rich variation in dynamics across the countries. For example, looking at column 1, the coefficients on lagged inflation in Table 1 range from.480 to.931. However, the indicator WEAK generates a range of only.667 to.775. Like findings pertain to the responses to DOIL and to DCOM. While we only report the results for WEAK as the indicator variable, the findings are similar for the other indicator variables as well. The estimates in Table 1 are at odds with another prediction of the theoretical model. Since the model predicts that inflation persistence and the response to oil and commodity price shocks are affected in the same way by the weight conservativeness of the central bank, one would expect the estimated coefficients on lagged inflation, oil prices, and commodity prices in Table 1 to be positively correlated. This is not the case: the correlations between the coefficients on lagged inflation and those on commodity prices is 0.06; for the coefficients on lagged 16

18 inflation and oil prices the correlation is 0.51; and for the coefficients on oil prices and commodity prices the correlation is Why does the model fail to capture the extent of variation in inflation dynamics across countries? One likely reason is that the standard indicators of the strength of the central bank s commitment to low inflation are too crude to capture some of the cross country differences that exist. Another possibility is that variables unrelated to the central bank s commitment to low inflation, such as wage-setting institutions or other structural factors, are a more important determinant of inflation dynamics. We investigate some of these alternative explanations below. 5. Robustness of Results In this section we alter the regressions in Table in a number of ways to verify the robustness of the results reported in the previous section. Table 6 drops U.S. data from the sample and adds the U.S. inflation rate as an additional control variable. We do this for two reasons. First, United States inflation may be an important predictor of inflation in other countries. Second, we want to control for the possibility that the oil and commodity price variables reflect the endogenous response of raw materials prices to U.S. inflation and have no direct effect on inflation in other countries. The evidence presented in the table suggests that U.S. inflation does have an important effect on foreign inflation rates: on average, a one percent increase in lagged U.S. inflation is correlated with a 0. percent increase in foreign inflation after one year. The introduction of U.S. inflation has very little effect on the coefficients on the economic variables. In almost every case, the coefficients on the interaction terms retain the sign and significance they held in Table. The only exception is the coefficient on the interaction between weakness and oil prices: this 17

19 coefficient remains positive, but becomes statistically insignificant when U.S. inflation is included in the regression. The regressions in Table exclude non-political variables that the theoretical model suggests affect the response of inflation to oil and commodity price shocks. For example, the effect of oil and commodity price shocks on unemployment may be larger in countries with very rigid nominal wages and prices. This would cause unemployment-averse central banks to inflate more in response to these shocks. Also, some countries in our sample were net exporters of commodities or oil for some part of our sample period. While increases in world oil and commodity prices might still be inflationary for those countries, the terms of trade effects might modify the magnitude or direction of the final effect on inflation. Table 7 attempts to control for these possibilities by adding two variables to the regressions in Table : an index of nominal wage flexibility (NWAGE) and a dummy variable for countries that are net exporters of fuel (OILEXP) or commodities (COMEXP). The index of nominal wage flexibility is from Bruno and Sachs (1985). It ranges from zero to six, with high values signifying greater flexibility. The oil export dummy equals one for the United Kingdom, Norway, and Netherlands and the commodity export dummy equals one for Australia, Canada, and New Zealand. 14 The variables are entered directly in the regressions. NWAGE is also interacted with inflation, oil prices, and commodity prices. OILEXP is interacted with the oil price variable and COMEXP is interacted with the commodity price variable. As one would expect, more wage flexibility is associated with a smaller response of inflation to commodity price shocks. This effect is statistically significant. In three out of four regressions nominal wage flexibility is found to reduce the degree of inflation persistence, but 18

20 this effect is not statistically significant. There is essentially no effect of wage flexibility on the response to oil shocks. Commodity price increases have a smaller effect on inflation in the commodity exporters than in other countries. Oil price increases have a modestly larger effect on inflation in oil exporting countries, but this effect is only marginally significant. The results regarding the interactions between political and economic variables are essentially unchanged by the inclusion of these new conditioning variables. The extended model also does a poor job of accounting for the cross-country differences in inflation dynamics shown in Table 1. The bottom panel of Table 5 reports summary statistics for the simulated coefficients derived from Table 7. Here, variation in the response of inflation to lagged inflation and price shocks is driven by differences in wage flexibility and a country s status as an importer or exporter of commodities and oil. Again, the variation in the simulated coefficients is too small to hope to explain a significant portion of the variation in the coefficients in Table 1. Simple OLS regressions of the Table 1 coefficients on the simulated coefficients show that the model in Table 7 can explain 18 percent of the cross-country variation in the response to oil prices, 31 percent of the variation in the response to commodity prices, but only three percent of the variation in inflation persistence. It is important to verify that the results in Table are not driven by a single country or time period. Table 8 summarizes a set of tests for country and period sensitivity. Column 1 repeats the full sample estimates of the interaction coefficients from Table. Columns and 3 show the minimum and maximum values that these coefficients take on as we sequentially drop five-year periods from the sample. Columns 4 and 5 show the minimum and the maximum coefficient values from experiments in which individual countries are dropped from the sample. 14 The determination of which countries are net oil and commodity exporters is made on the basis of World Bank data on fuel and primary commodity imports and exports. The World Bank categories are not exactly the same as 19

21 The coefficient estimates hold up fairly well to the exclusion of five-year time periods from the sample. The effect of the weakness index is always positive, though the magnitude varies considerably. The effect of CBI is always to reduce the inflationary response to lagged inflation or price shocks, except that when is dropped from the sample there is a small positive effect on the response to oil price shocks. The effect of FREQ is uniformly positive, except that the effect on the response to commodity price shocks disappears when the period is dropped from the sample. Dropping five-year sub-periods does not change the coefficients on the interactions involving ORIENT, but these were never strong to begin with. The coefficient estimates are also not substantially affected when individual countries are dropped from the sample. This is especially true as far as the index of weakness and political instability are concerned. Not only are the estimates uniformly positive, but they are confined to a relatively small range. The estimates of the effect of political orientation are consistent as well. The estimates of the effect of CBI on inflation persistence appear more problematic. When Spain is dropped from the sample, the coefficient on the interaction between CBI and lagged inflation becomes slightly positive and statistically insignificant. It turns out, however, that this result in turn hinges entirely on whether a single observation, Japan 1975, is included in the sample. When Japan 1975 is dropped, the interaction between CBI and lagged inflation becomes negative and significant once again. In fact, all of the results in Table are strengthened when this one observation is dropped. The reason that this single observation has such a disproportionate effect must be the unusually large decline in inflation in Japan from 1974 to 1975 (from 0.8 percent to 11.1 percent). 6. Conclusions the oil and commodity price variables we use in our regressions, but they are a reasonable approximation. 0

22 The data support the hypothesis that dynamics of inflation in the OECD countries are significantly related to variables that signal a central bank s ability to commit to low inflation. Central banks that operate without a strong mandate for low inflation because of a lack of independence from the government and/or political instability tend to inflate more in response to oil and commodity price shocks and suffer a greater degree of inflation persistence. The ideological orientation of the government, while it affects average inflation and inflation persistence, does not have a consistent effect on the inflationary response to oil and commodity price shocks. An index of weakness with regard to inflation control has especially strong effects on the dynamics of inflation. The empirical work presented here, however, also shows that the variables typically used to represent a central bank s institutional commitment to low inflation do not explain the range of inflation dynamics across countries that we see in Table 1. Better measures of political and structural susceptibility to inflationary pressures will be required if the time consistency model is to explain why inflation dynamics vary so substantially across countries. 1

23 Acknowledgements The authors are grateful for comments and suggestions by participants at the Midwest Macroeconomics Conference at the University of Pittsburgh and the Theories and Methods in Macroeconomics Conference at the Université du Quebec à Montreal, and at seminars at Johns Hopkins University and Virginia Commonwealth University. All errors and omissions are our own.

24 Appendix A. Proofs regarding theoretical model. A.1 Unique stable solution to equation (10). Equation (10) is repeated here for convenience. c = α λθ(1-c)[1-βc -βθ(1-c)c] f(c) (A.1.1) A stable solution requires that c <1. Proposition: For all α>0, λ>0, θ (0,1), β (0,1), there exists exactly one value of c (0,1) that satisifies equation (A.1.1). Presentation of the proof is assisted by Figure A1, which plots c and f(c) against c for arbitrary parameter values (α=1, λ=1, θ=0.5, β=0.9). The solutions to equation (A.1.1) are represented by the intersections of the f(c) curve with the forty-five degree line. The proof proceeds in five stages. (i) (ii) f(0) = α λθ > 0 (shown as point A on Figure A1). f(1) = 0 (shown as point B on Figure A1). These remarks are apparent from equation (A.1.1). (iii) f(c) has two inflection points, one positive and one negative. The fact that there are two inflection points follows from the function being a cubic polynomial. Taking the derivative of f(c) with respect to c and setting it equal to zero, we find that the two inflection points are given by c c + 1 = 3β(1 θ) 1 = 3β(1 θ) ( β(1 θ) + 4β (1 θ) + 1β(1 θ)(1 + βθ) ) ( β(1 θ) 4β (1 θ) + 1β(1 θ)(1 + βθ) ) > 0 (A.1.a) < 0 (A.1.b) (iv) There is one value c (0,1) such that f(c)=c. It is easy to verify that f (0) 0 and f (1) 0. Given that the slope of f(c) is negative at c=0 and c=1, if there are any inflection points between 0 and 1 there must be an even number of them. Since there is only one positive inflection point on f(c), there cannot be an inflection point between 0 and 1. Since f(c) is continuous and negatively sloped between points A and B, it must cross the forty-five degree line in the interval c (0,1). 3

25 (v) There is no solution c (-1,0). This can be verified by inspection of equation (A.1.1). If c (-1,0), then 1-c>0, 1-βc >0, and - βθ(1-c)c>0, so f(c)>0. But then f(c) c. A. Derivatives of coefficient on lagged inflation in optimal policy function Proposition: For all α>0, λ>0, θ (0,1), β (0,1), c/ λ>0. This can be shown from inspection of equation (A.1.1) and Figure A1. It is clear that when c (0,1), f/ λ>0. When λ increases the f(c) curve pivots around point B and rotates up in the interval (0,1) (point A moves up the vertical axis). This causes f(c) to intersect the forty-five degree line at a larger value of c. 4

26 Figure A1. Solutions to equation (11) with α=1, λ=1, θ=0.5, β= f(c) 4 3 c 1 A B c

27 Appendix B: Data description INF: Year-to-year percentage change in CPI, from IMF International Financial Statistics CD- ROM. UR: Civilian unemployment rate from Jackman et al. (1994). DOIL: Year-to-year percentage change in oil prices. From DRI database, series PW561. DCOM: Year-to-year percentage change in export commodity prices, in current dollars. From IMF IFS on CD-ROM, line 00176axd. CBI: Cukierman s (199) measure of legal independence. Cukierman reports separate values for the subperiods , , and For the years , we use the values of Cukierman s index. Larger values of the index imply greater independence. FREQ: Average number of government changes per year in the preceding five years. Government change is defined as change in the party of the executive branch (for presidential systems) or ruling party of legislature (for parliamentary systems). For years , average number of changes over is used. Data were provided to us by Phillip Swagel. The original source is Jodice and Taylor (1983). We updated this using Banks (various issues). ORIENT: Dummy variable equal to +1 if the ruling party is right-wing, -1 if it is left-wing. From Alesina and Roubini (1997). USINF: U.S. CPI inflation rate, from IMF International Financial Statistics CD-ROM. NWAGE: Index of nominal wage rigidity from Bruno and Sachs (1986). OILEXP: Dummy variable equal to 1 for Netherlands, Norway, United Kingdom. COMEXP: Dummy variable equal to 1 for Australia, Canada, New Zealand. 6

28 Table B1. Country averages of select variables. Standard deviations in parentheses. Country INF CBI FREQ ORIENT WEAK a Australia 6.8 (3.87) 0.31 (0.0000) 0.30 (0.4) (0.14) Austria 4.9 (1.85) 0.61 (0.0445) 0.7 (0.18) (0.14) Belgium 4.65 (.79) 0.18 (0.0059) 0.38 (0.0) (0.14) Canada 5.17 (.99) 0.46 (0.0000) 0.6 (0.13) (0.1) Denmark 6.48 (3.06) 0.47 (0.0000) 0.36 (0.3) (0.13) Finland 6.93 (3.78) 0.7 (0.0000) 0.46 (0.8) (0.13) France 6.07 (3.4) 0.8 (0.0033) 0.35 (0.16) (0.1) Germany 3.45 (1.71) 0.66 (0.0000) 0.34 (0.30) (0.10) Italy 8.36 (5.34) 0. (0.0000) 0.68 (0.19) (0.1) Japan 5.10 (3.93) 0.16 (0.0000) 0.41 (0.3) (0.11) Netherlands 4.39 (.65) 0.4 (0.0000) 0.3 (0.3) (0.1) New Zealand 7.90 (4.8) 0.7 (0.0000) 0.3 (0.1) (0.14) Norway 6.4 (.84) 0.13 (0.0098) 0.5 (0.17) (0.13) Spain 9.30 (4.73) 0.15 (0.055) 0.7 (0.30) NA NA NA NA Sweden 6.56 (.87) 0.7 (0.0000) 0.35 (0.3) (0.13) Switzerland 3.87 (.03) 0.61 (0.063) 0.48 (0.39) (0.1) United Kingdom 7.34 (4.75) 0.36 (0.0790) 0.4 (0.15) (0.13) United States 4.80 (.91) 0.51 (0.0000) 0.3 (0.1) (0.11) Cross-section 5.96 (1.6) 0.35 (0.17) 0.34 (0.11) (0.08) Sample range is or shorter, depending on data availability. Bottom row gives mean and standard deviation (in parentheses) of country averages. a Weakness index derived from Hauser-Goldberger procedure. Based on regression of average inflation rate (by country and decade) on decade dummies, CBI, FREQ, and ORIENT. 7

29 References Alesina, A., Roubini, N., Political Cycles and the Macroeconomy. MIT Press, Cambridge, MA. Avery, R, Modeling monetary policy as an unobserved variable. Journal of Econometrics 1 (3), Backus, D., Driffill, J., Inflation and reputation. American Economic Review 75 (3), Ball, L., Time-consistent policy and persistent changes in inflation. Journal of Monetary Economics 36 (), Banks, J., Political Handbook of the World. CSA Publications, New York, NY. Barro, R., Reputation in a model of monetary policy with incomplete information. Journal of Monetary Economics 17 (1), 3-0. Barro, R., Gordon, D., A positive theory of monetary policy in a natural rate model. Journal of Political Economy 91 (4),