Final draft

The Role of Theory-Motivated Fundamentals in Long-Run Exchange Rate Forecasting7. Annual Frequency (Bank of England) Exchange Rate ForecastingResults Moving beyond what has largely been attended to in the literature, it is appropriate to test theefficacy of the hybrid theory model on truly long-run data with longer-term forecasts. While this analysisis restricted to dollar-sterling exchange rates due to availability of data, it provides possible insight intothe evolution of forecasts beyond horizons typically examined in the literature today. 2018 APRIL|InFER 49

50 InFER|2018 APRIL Figure 27: Hybrid Model Forecasting Regression Output (1- to 12-Year Ahead Forecast Horizons) – Full Sample, 1861-2015 Dependent Variable: Log of Dollar-Sterling Exchange Rate k-years ahead 12 3 45 67 8 9 10 11 12 Log(P/P*) 0.154*** 0.407*** 0.579*** 0.679*** 0.71*** 0.673*** 0.567*** 0.485*** 0.513*** 0.574*** 0.593*** 0.585*** (0.051) (0.108) (0.153) (0.186) (0.198) (0.185) (0.167) (0.155) (0.158) (0.163) (0.173) (0.194) Log($/£) 0.836*** 0.562*** 0.373** 0.26 0.221 0.257 0.367** 0.452*** 0.418** 0.351** 0.328* 0.333 (0.053) (0.112) (0.156) (0.187) (0.199) (0.192) (0.179) (0.168) (0.167) (0.168) (0.18) (0.204) Constant -0.059** -0.144*** -0.204*** -0.241*** -0.255*** -0.247*** -0.219** -0.198** -0.212** -0.238** -0.249** -0.249** (0.028) (0.054) (0.074) (0.089) (0.095) (0.09) (0.086) (0.087) (0.095) (0.102) (0.109) (0.116) Observations 154 153 152 151 150 149 148 147 146 145 144 143 R2 0.974 0.942 0.924 0.91 0.904 0.894 0.883 0.869 0.078 0.117 0.133 0.925 0.919 0.912 0.91 0.139 0.143 0.15 0.158 0.166 RMSE 0.13 0.134 0.139 0.14 HAC robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Figure 28: Univariate Autoregressive Forecasting Model & Diebold-Mariano Tests (1- to 12-Year Ahead Forecast Horizons) – Full Sample, 1861-2015 Dependent Variable: Log of Dollar-Sterling Exchange Rate k-years ahead 12 3 45 67 8 9 10 11 12 DM Constant -0.0002 -0.0016* -0.0033* -0.0047* -0.0053* -0.0049* -0.0037 -0.0031 -0.0035 -0.0043 -0.0047 -0.0048 (0.0002) (0.0009) (0.0019) (0.0027) (0.0031) (0.0028) (0.0023) (0.0022) (0.0024) (0.0028) (0.0031) (0.0035) Log($/£) 0.993*** 0.979*** 0.97*** 0.967*** 0.966*** 0.970*** 0.977*** 0.981*** 0.979*** 0.977*** 0.975*** 0.973*** (0.014) (0.025) (0.033) (0.041) (0.047) (0.053) (0.057) (0.058) (0.058) (0.06) (0.062) (0.066) Constant 0.001 0.012 0.015 0.012 0.006 -0.006 -0.022 -0.034 -0.037 -0.039 -0.044 -0.047 (0.018) (0.033) (0.044) (0.053) (0.061) (0.068) (0.073) (0.074) (0.074) (0.076) (0.08) (0.085) Observations 155 155 155 155 155 155 155 155 155 155 155 155 R2 0.973 0.935 0.906 0.865 0.855 0.841 0.829 0.815 0.079 0.123 0.148 0.888 0.874 0.866 0.865 0.177 0.184 0.192 0.199 0.207 RMSE 0.162 0.158 0.171 0.177 HAC robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1

The Role of Theory-Motivated Fundamentals in Long-Run Exchange Rate Forecasting In applying the same methodology to the annual bilateral dollar-sterling exchange rate and pricedata from the Bank of England dataset, first with the full sample from 1861-2015, the following patternof exchange rate coefficients borne out in the data is as follows:βk Figure 29: Evolution of Coefficients for USD/GBP Forecasts - Full Bank of England Dataset Sample, 1861-2015 - HAC Error Bars 12 Lagged USD/GBP XR P/P* 1.2 1 0.8 0.6 0.4 0.2 0 0 2 4 6 8 10 k-years It is immediately apparent that the trajectory of coefficients observed at the monthly frequencies inthe 5-year forecasting horizon from above does not hold consistently as that horizon increases. It isimportant to keep in mind, this analysis pertains to a vastly different dataset, with different frequenciesof data and steeper increases in the forecast horizon. Institutional effects notwithstanding (more on thisbelow), there is a steady, almost parabolic, pattern of these theory coefficients as lags increase, which peakat 0.71013 in this sample at the 5-year ahead forecast horizon. This contribution decreases modestlybetween the fifth and eighth periods and then rises again, seemingly steadying at approximately 0.60.Overall, the trend is positive, which suggests that the theory component of the hybrid exchange ratemodel contributes to predictive power in forecasting future exchange rates relative to the random walkeven with this stark change in data and forecasting horizons. This is particularly notable in the long-run as the distance between the forecasted exchange rate andthe current exchange rate increases. The first-period forecasted ������������������������ (0.15425) is significant at the 95%significance level, and all preceding forecasted ������������������������’s from lag 2 through 12 are significant at the 99% level.As such, the role that purchasing power parity, as the theory component of this hybrid exchange rateforecasting model, is far from trivial economically, and is robustly significant, strengthening theargument that the inclusion of a fundamental does in fact improve upon the parsimonious random walkmarkedly. 2018 APRIL|InFER 51

RESEARCH Note, further, from the figure above that the coefficients for the random walk component mirrorthose of the theory component even in the parabolic pattern as the number of lags increases. As therelative role of theory increases, the role of the past decreases and vice versa. The random walkcomponent of the regression equation and its coefficients are not as statistically robust as the theorycomponent as detailed above. While all coefficients across the 12 lags are statistically significant, at leastat the 90% level, there is less evidence of the remarkable statistical significance that prevailed in lags 2through 11 of the theory coefficients. Thus, while the role of the past exchange rate series componentbecomes less relevant in its contribution to the predictive power of the forecast as lags increase, thecontribution is both statistically and economically significant. Figure 30: Model Fit for USD/GBP Forecasts - R2 and Root Mean Squared Error - Full Bank of England Dataset Sample, 1861-2015 R-squared RMSFE 0.98 0.2 0.96 0.15 0.94 0.92 0.1 0.9 0.05 0.88 0.86 0 0 2 4 6 8 10 12 k-lags In accordance with assessments of model fit from the four currencies of analysis with monthly data,I defer to plots of R2 and RMSE over the course of the 12 lags, as above. Consistent with the results above,the plot suggests that the model loses explanatory power over the time-horizon, and the RMSEs of theforecasts increase. The explanatory power of the model, as indicated by R2 decreases as lags are added—from a remarkable fit of 0.97 down to 0.87 over the course of the 12 lags. Compared to the deteriorationof explanatory power exhibited in the monthly analysis, however, this is the most robust trajectory ofR2 yet—note that, in conducting a forecast that is 12-years ahead given price and exchange rate data today,the forecasting model only loses 0.1 in terms of R2, i.e. explanatory power. This is striking, especiallyconsidering the displacement in the data for these long-horizon forecasts. RMSE expectedly increasesover the course of the 12 lags, beginning at 0.078 and ending at 0.166. These levels are well in-line withthose of the monthly forecasts and, relatively speaking, the model has not deteriorated any more rapidlythan the 5-year ahead monthly forecasts. I suspect however, given these results, the trend of increasingRMSE and decreasing R2 continues beyond the 12-year ahead forecast. Overall, despite the possibleimpact of institutional considerations discussed above, the hybrid model performs remarkably well withthese truly long-horizon forecasts given the long-run data sample.52 InFER|2018 APRILR-squared RMSFE

The Role of Theory-Motivated Fundamentals in Long-Run Exchange Rate Forecasting One possible explanation for the deterioration of explanatory power and increasing RMSE withlarge displacements in time could be the role of institutions in determining exchange rates independentlyof the theory that underlies this model as discussed in the Data Description section. It is reasonable toassume that attempting to forecast exchange rates under one exchange rate regime may be error-pronewhen using exchange rate data from another. This would be especially apparent when forecasting onhorizons of 10-12 years ahead when markedly different economic institutions/exchange rate regimes, insome instances, only span the length of 30 years (i.e. the Bretton Woods era). While I provide economic justifications of the choice of years for subdividing the broader datasetin the Data Description section above, it is prudent to evaluate to what extent those choices areempirically motivated by the data itself. Quandt-Andrews unknown breakpoint tests behave, generally,as simple Chow structural break tests but utilize a more penalizing critical value table making it moredifficult for the null of no structural break to be rejected. Using Quandt-Andrews unknown breakpointtests on the entire sample (trimmed by 15% on either extreme), I reject the null hypothesis of no structuralbreak at the 95% level with respect to an underlying structural break at 1949. Results from Quandt-Andrews unknown breakpoint test are as follows:Figure 31: Quandt-Andrews Unknown Breakpoint Tests for annual USD/GBP Exchange Rate Series Null Hypothesis: No breakpoints within 15% trimmed dataEquation Sample: 1861-2015 1939-2015Test sample: 1885-1992 1951-2004 t-value p-value t-value p-valueMaximum Wald F-statistic (1949) 11.090 0.016 Maximum Wald F-statistic (1974) 6.503 0.129Exp Wald F-statistic 2.634 0.024 Exp Wald F-statistic 1.480 0.101Ave Wald F-statistic 2.990 0.045 Ave Wald F-statistic 1.662 0.160 I defer to the Maximum Wald F-statistic when drawing conclusions about the empirical evidenceof structural breaks. While the 1949 structural breakpoint from the full sample is five years ahead of mychoice of 1944 for the Bretton Woods period, I see it as justification, broadly, for the fundamentallydifferent institutional and economic considerations that this period exhibits. Since the choice of 1944 ismotivated specifically with the conception and implementation of the system, I will continue to use thisdate as the start of the period, but do argue the results of the break test substantiate the use of this separatesubperiod generally. Seeking further empirical justification for more recent structural breaks, I conduct the same testmethodology on the 1939-2015 sample (Bretton Woods to present day). In this sample, the mostsignificant break presented is for 1974, in line with the breakdown of the Bretton Woods system, but thebreak is not statistically significant at the 90% level with a t-value of only 1.480. Still, the choice of thisyear serves as further motivation for the choice of these subdivisions. I attend, now, to regression outputfrom the subperiods and corresponding plots as above. 2018 APRIL|InFER 53

54 InFER|2018 APRIL Figure 32: Hybrid Model Forecasting Regression Output (1- to 12-Year Ahead Forecast Horizons) – Gold Standard, 1861-1939 Dependent Variable: Log of Dollar-Sterling Exchange Rate k-years ahead 12 3 45 67 8 9 10 11 12 Log(P/P*) 0.12 0.295 0.321 0.292 0.242 0.171 0.058 -0.008 0.003 0.046 -0.028 -0.091 (0.085) (0.187) (0.215) (0.188) (0.172) (0.132) (0.102) (0.088) (0.075) (0.089) (0.081) (0.098) Log($/£) 0.718*** 0.333 0.189 0.16 0.129 0.123 0.205* 0.271** 0.246*** 0.182** 0.278*** 0.321** (0.136) (0.232) (0.238) (0.227) (0.221) (0.161) (0.106) (0.11) (0.084) (0.081) (0.096) (0.147) Constant 0.209* 0.473*** 0.647*** 0.742*** 0.887*** 1.039*** 1.132*** 1.155*** 1.168*** 1.181*** 1.177*** 1.233*** (0.106) (0.112) (0.141) (0.14) (0.122) (0.093) (0.099) (0.105) (0.093) (0.096) (0.109) (0.123) Observations 78 77 76 75 74 73 72 71 70 69 68 67 R2 0.706 0.427 0.32 0.203 0.219 0.201 0.239 0.214 0.079 0.111 0.117 0.37 0.308 0.217 0.183 0.075 0.068 0.067 0.065 0.065 RMSE 0.093 0.088 0.088 0.084 HAC robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Figure 33: Univariate Autoregressive Forecasting Model & Diebold-Mariano Tests (1- to 12-Year Ahead Forecast Horizons) – Gold Standard, 1861-1939 Dependent Variable: Log of Dollar-Sterling Exchange Rate k-years ahead 12 3 45 67 8 9 10 11 12 DM Constant -0.0001 -0.0006 -0.0007 -0.0006 -0.0004 -0.0002 0.000 0.000 0.000 0.000 0.000 -0.0001 (0.0002) (0.0008) (0.001) (0.0008) (0.0006) (0.0003) (0.000) (0.000) (0.000) (0.0001) (0.0001) (0.000) Log($/£) 0.841*** 0.63*** 0.505*** 0.433*** 0.345*** 0.261*** 0.221*** 0.202*** 0.178*** 0.157** 0.171 0.147 (0.073) (0.076) (0.122) (0.069) (0.074) (0.07) (0.051) (0.05) (0.066) (0.066) (0.075) (0.104) Constant 0.256** 0.596*** 0.797*** 0.913*** 1.055*** 1.192*** 1.255*** 1.285*** 1.323*** 1.358*** 1.335*** 1.374*** (0.113) (0.118) (0.114) (0.126) (0.122) (0.098) (0.103) (0.131) (0.131) (0.143) (0.185) (0.212) Observations 79 79 79 79 79 79 79 79 79 79 79 79 R2 0.697 0.385 0.244 0.024 0.016 0.009 0.013 0.006 0.08 0.113 0.12 0.176 0.107 0.055 0.035 0.075 0.068 0.067 0.065 0.065 RMSE 0.096 0.091 0.089 0.084 HAC robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1

Figure 34: Hybrid Model Forecasting Regression Output (1- to 12-Year Ahead Forecast Horizons) – Bretton Woods, 1944-1973 Dependent Variable: Log of Dollar-Sterling Exchange Rate k-years ahead 12 3 45 67 8 9 10 11 12 Log(P/P*) -0.042 -0.085 -0.137 -0.079 0.051 0.17 0.271 0.445** 0.676*** 0.775*** 0.87*** 1.061*** (0.108) (0.225) (0.329) (0.334) (0.283) (0.255) (0.235) (0.207) (0.241) (0.243) (0.24) (0.286) Log($/£) 0.938*** 0.863*** 0.817*** 0.736*** 0.626** 0.522* 0.433* 0.319* 0.192 0.152 0.085 -0.067 (0.258) (0.23) (0.178) (0.154) (0.139) (0.123) (0.143) (0.095) (0.182) (0.233) (0.26) (0.271) Constant 0.116 0.25 0.369 0.358 0.266 0.183 0.114 -0.043 -0.28 -0.408 -0.494 -0.636* (0.136) (0.28) (0.411) (0.449) (0.388) (0.327) (0.286) (0.272) (0.306) (0.31) (0.313) (0.357) Observations 30 30 30 30 30 30 30 30 30 30 30 30 R2 0.896 0.763 0.66 0.591 0.683 0.754 0.728 0.69 0.053 0.08 0.096 0.565 0.528 0.521 0.541 0.105 0.092 0.081 0.085 0.091 RMSE 0.108 0.113 0.113 0.111 HAC robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Figure 35: Univariate Autoregressive Forecasting Model & Diebold-Mariano Tests (1- to 12-Year Ahead Forecast Horizons) – Bretton Woods, 1939-1973 Dependent Variable: Log of Dollar-Sterling Exchange Rate k-years ahead 12 3 45 67 8 9 10 11 12 DM Constant 0.000 0.000 -0.0001 0.000 0.000 -0.0002 -0.0005 -0.0012 -0.0026* -0.0032* -0.004** -0.007 (0.0006) (0.0003) (0.0002) (0.0006) (0.0008) (0.0011) (0.0015) (0.0016) (0.0017) (0.0042) (0.0001) (0.0003) Log($/£) 0.91*** 0.812*** 0.740*** 0.693*** 0.655*** 0.619*** 0.589*** 0.573*** 0.574*** 0.58*** 0.560*** 0.492***2018 APRIL|InFER 55 (0.084) (0.155) (0.2) (0.234) (0.233) (0.209) (0.185) (0.169) (0.162) (0.152) (0.153) (0.153) Constant 0.082 0.175 0.242 0.284 0.313 0.340 0.364* 0.372* 0.360* 0.341* 0.359* 0.442** (0.083) (0.156) (0.203) (0.242) (0.244) (0.224) (0.201) (0.189) (0.186) (0.18) (0.181) (0.176) Observations 30 30 30 30 30 30 30 30 30 30 30 30 R2 0.892 0.753 0.643 0.529 0.571 0.622 0.567 0.411 0.053 0.08 0.096 0.548 0.51 0.496 0.506 0.11 0.105 0.099 0.106 0.124 RMSE 0.108 0.113 0.114 0.113 HAC robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1

56 InFER|2018 APRIL Figure 36: Hybrid Model Forecasting Regression Output (1- to 12-Year Ahead Forecast Horizons) – Current Float, 1974-2015 Dependent Variable: Log of Dollar-Sterling Exchange Rate k-years ahead 12 3 45 67 8 9 10 11 12 Log(P/P*) 0.141 0.504*** 0.843*** 1.003*** 0.994*** 0.825*** 0.544*** 0.296** 0.232* 0.29 0.319 0.241 (0.1) (0.119) (0.141) (0.173) (0.168) (0.149) (0.134) (0.113) (0.137) (0.193) (0.208) (0.171) Log($/£) 0.684*** 0.177* -0.278*** -0.539*** -0.59*** -0.433*** -0.127 0.115 0.129 0.01 -0.07 -0.02 (0.091) (0.095) (0.102) (0.169) (0.186) (0.152) (0.127) (0.104) (0.099) (0.17) (0.185) (0.107) Constant 0.032 -0.031 -0.099 -0.108 -0.077 -0.012 0.074 0.165* 0.216* 0.228* 0.247* 0.291** (0.068) (0.097) (0.104) (0.092) (0.092) (0.104) (0.103) (0.097) (0.111) (0.128) (0.138) (0.14) Observations 42 42 42 42 42 42 42 42 42 42 42 42 R2 0.661 0.366 0.364 0.353 0.3 0.237 0.192 0.154 0.077 0.106 0.106 0.504 0.57 0.498 0.391 0.107 0.111 0.116 0.12 0.122 RMSE 0.094 0.087 0.094 0.104 HAC robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Figure 37: Univariate Autoregressive Forecasting Model & Diebold-Mariano Tests (1- to 12-Year Ahead Forecast Horizons) – Current Float, 1974-2015 Dependent Variable: Log of Dollar-Sterling Exchange Rate k-years ahead 12 3 45 67 8 9 10 11 12 DM Constant -0.0001 -0.0014* -0.0047** -0.0082** -0.0093** -0.0071** -0.003** -0.0009 -0.0005 -0.0009 -0.001 -0.0006 (0.0001) (0.0007) (0.002) (0.0037) (0.004) (0.0029) (0.0015) (0.0007) (0.0007) (0.0011) (0.0013) (0.0008) Log($/£) 0.752*** 0.461*** 0.256* 0.164 0.164 0.235 0.329** 0.367*** 0.331*** 0.267** 0.216 0.199 (0.188) (0.206) (0.19) (0.151) (0.114) (0.105) (0.121) (0.134) (0.135) (0.062) (0.1) (0.152) Constant 0.122*** 0.275*** 0.384*** 0.434*** 0.433*** 0.389*** 0.329*** 0.303*** 0.322*** 0.36*** 0.389*** 0.398*** (0.034) (0.054) (0.077) (0.094) (0.105) (0.104) (0.093) (0.075) (0.062) (0.065) (0.073) (0.074) Observations 42 42 42 42 42 42 42 42 42 42 42 42 R2 0.648 0.268 0.075 0.019 0.284 0.251 0.169 0.112 0.099 0.078 0.112 0.126 0.13 0.022 0.076 0.197 0.111 0.114 0.116 0.124 0.125 RMSE 0.13 0.126 0.118 HAC robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1

The Role of Theory-Motivated Fundamentals in Long-Run Exchange Rate Forecasting For the sake of brevity and ease of comparison, I plot the coefficient evolution of purchasing powerparity and lagged exchange rates for each subperiod in one summary graphic—connecting lines betweendata points have been added for clarity. Deferring to the analysis presented in the Data Description, 1861-1939 is considered the Gold Standard (“GS”), 1944-1973 is considered the Bretton Woods era (“BW”),and 1974-2015 is the current float (“Float”). Figure 38: Evolution of Coefficients for USD/GBP Forecasts Lagged USD/GBP XR - GS - 1861-1939 P/P* - GS - 1861-1939 Lagged USD/GBP XR - BW - 1944-1973 P/P* - BW - 1944-1973 Lagged USD/GBP XR - Float - 1974-2015 P/P* - Float - 1974-2015 1.2R-squared βk 1 RMSFE 2 4 6 8 10 12 0.8 k-years 0.6 0.4 0.2 0-0.2-0.4-0.6 0 Figure 39: Model Fit for USD/GBP Forecasts - R2 and RMSE R-squared - GS - 1861-1939 R-squared - BW - 1944-1973 R-squared - Float - 1974-2015 RMSFE - GS - 1861-1939 RMSFE - BW - 1944-1973 RMSFE - Float - 1974-2015 1 0.140.90.8 0.120.70.6 0.10.50.4 0.080.30.2 0.060.1 0.04 0 0 0.02 0 2 4 6 8 10 12 k-years 2018 APRIL|InFER 57

RESEARCH It is immediately apparent that the consistency of results from the monthly analysis and full sampleannual analysis falls apart when the sample is broken up into subperiods.7 I find dramatically differenttrajectories for coefficient estimates across forecast horizons and for metrics of explanatory power andforecast accuracy—this implies that the results are highly sensitive to the underlying institutionalconsiderations and, furthermore, the “fundamental” that underlies the broader sample is likelyfundamentally different than that which is observed in each distinct subperiod. With respect to the Gold Standard, the ������������������������ coefficient is never statistically significantly differentfrom zero at any forecast horizon, and therefore does not contribute any meaningful predictive powerto the hybrid model in this context. This consideration notwithstanding, the magnitude of thecoefficient rises only through the 3-year ahead forecast horizon, peaking at only approximately 0.3, andthen declining unequivocally as the horizon increases from there. Incidentally, the coefficient for therandom walk component does not precisely mirror these movements, in stark contrast to other samples.Moreover, the coefficient only becomes significant at the 90% level at the 7-year ahead forecast horizon.Rather than exhibiting a decline in the contribution of the past, the Gold Standard sample featuresincreasing contribution at longer-horizons in a statistical sense. This may imply that either thepurchasing power parity fundamental is not applicable as a theory variable in this instance, or thespecification is inappropriate for the sample. In terms of forecast accuracy and model fit, R2 declinesthroughout the sample to 0.214 at the 12-year ahead forecast horizon, and RMSE, surprisingly, declinessomewhat as the horizon increases. I posit this is likely due to the eventual significance of the randomwalk component at longer horizons as described above. Further, the hybrid theory model does notperform statistically significantly better than the univariate autoregressive model per the results ofDiebold Mariano tests.8 Results from the Bretton Woods era are more in line with those observed in the full and monthlysamples as above. The contribution of theory via the ������������������������ coefficient increases in statistical and economicsignificance as the forecast horizon increases, becoming significant at the 99% level at the 9-year aheadhorizon and reaching 1.06 in magnitude at the 12-year ahead forecast horizon. The contribution of therandom walk more appropriately mirrors that of purchasing power parity, beginning close to 1 anddecreasing in economic and statistical significance with increasing displacements in the forecast horizon.These results are highly complementary. As regression output included in the Appendix will show, onlythe 7-year ahead forecast incorporates statistically significant contributions from both components—prior to this horizon, only the past exchange rate contributes meaningfully, with the theory componentdriving the forecasts from 8-years ahead and beyond. Evaluation metrics are far more like those of the monthly and full sample annual analyses as well.RMSE increases rapidly at the onset of the forecasts, peaking at 0.113 in the 6-year ahead forecast and then7 Refer to Appendix for individual coefficient trajectory graphs with HAC error bars.8 Refer to Figures 33, 35, and 37 above for results of Diebold Mariano tests for annual USD/GBP exchange rate forecasts.58 InFER|2018 APRIL

The Role of Theory-Motivated Fundamentals in Long-Run Exchange Rate Forecastingdecreasing somewhat. Correspondingly, the R2 of the forecasts steadily decreases through the 6-yearahead forecast and then increases. Note that as the role of the fundamental becomes statisticallysignificant, the forecasts improve (in the 8- to 10-year ahead forecast horizons), suggesting the BrettonWoods era may be particularly suited to this model given the relative constancy in exchange rates andprices. Since prices are likely to fluctuate more than exchange rates given the nature of the Bretton Woodsexchange rate regimes, it stands to reason that the exchange rate itself might be the best predictor in themedium-term and that the purchasing power parity component best captures what variations do presentin the truly long-horizon forecasts. Forecasts conducted during the current float are also more consistent with those from the monthlyfrequencies—I would expect to see a certain degree of similarity between the two forecasts for USD/GBPexchange rates through the 5-year horizon. In this spirit, the results are quite similar through theseforecast horizons, with the contributions of the random walk and theory mirroring each other moreprecisely than in other subdivided samples. The ������������������������ coefficient is significant at the 90% level for the 1-year ahead forecast horizon and rapidly approaches 1 by the four-year ahead horizon, declining inmagnitude and statistical significance thereafter, and offering no meaningful contribution at the 10-yearahead forecast horizon and beyond. The contribution of the random walk, much like in the monthlyanalysis, is statistically significant and negative from the 3-year ahead forecast to the 6-year ahead forecastand is insignificant thereafter. R2 values dip through the 2- and 3-year ahead forecast horizons and thenrecovers through the 5-year ahead, while RMSE drops somewhat at that horizon and then increasesindefinitely thereafter. These results potentially point to a general breakdown in the model past the 5- and 6-year timehorizons. This does not seem surprising given the highly volatile nature of exchange rates in the modernfloat—while it is promising that the hybrid model can improve upon the random walk in the medium-term, it is unclear that either model perform adequately in this environment beyond those horizons.Results from the Diebold Mariano tests, similarly, support a statistically valid improvement in accuracyrelative to the univariate autoregressive model in the 2-year to 7-year ahead forecasts, but neither modelis more or less accurate at longer forecast horizons.8. Cointegration and Vector Error Collection Models As mentioned briefly in the time-series properties section of this analysis, the existence ofcointegration between the fundamental and exchange rate series could provide additional predictivepower to existing forecasts and provide a sounder theoretical foundation for the results of the hybridspecification I utilize here. Two series are said to be cointegrated if both underlying series are I(1), but alinear combination of the two series is I(0), or stationary. As such, while little can be said of the long-runbehavior of a unit root series given its inherent non-stationarity, cointegrating series can provideinformation about where one of the underlying non-stationary series is headed in the long-run relativeto the other. In this context, the degree to which log purchasing power parity series and log bilateral 2018 APRIL|InFER 59

RESEARCHexchange rate series are cointegrated should serve as motivation for the use of the relative price ratio asthe underlying fundamental to which exchange rate deviations self-correct. By construction,cointegrating series should, to some extent, be self-correcting with respect to one another. Figure 40: Single-Equation Engle Granger Cointegration Test Results Null Hypothesis: Series are not cointegratedDependent Variable Tau-Statistic p-value Z-Statistic p-valueLog USD/CAD Exchange Rate -1.695 0.681 -5.902 0.656Log USD/CHF Exchange Rate -3.528 0.031 -19.577 0.059Log USD/JPY Exchange Rate -3.478 0.036 -17.36 0.091Log USD/GBP Exchange Rate -3.611 0.0248 -26.258 0.0142Note: The independent variable for all Single-Equation Engle Granger tests for cointegration is the correspondinglog purchasing power parity series for each exchange rate series. Using Single-Equation Engle Granger tests for cointegration, I reject the null of no cointegrationat the 90% significance level for all series except for that of the USD/CAD exchange rate and purchasingpower parity relationship, suggesting some fundamental differences in the two series that undermine thelong-term predictability of one series relative to the other. Broadly, though, the degree to which theexchange rate and purchasing power series are cointegrated is promising—we would expect that theinclusion of log purchasing power parity in the exchange rate forecast may provide additional empiricallyvalid predictive power about the long-run behavior of the exchange rate. To further motivate this intuition, and to more directly exploit the possible improvement inpredictive power vis-à-vis the cointegrating relationships developed herein, Vector Error-CorrectionModels (or VECMs) directly incorporate the co3integrating relationship for the forecasting of changesin cointegrating series. Broadly, I begin by estimating the cointegrating relationships between theexchange rate and relative price ratio series for the pound sterling, Japanese yen, and Swiss franc (as theCanadian series are not cointegrated) by estimating: ������������������������ = ������������ + ������������������������������������������������ + ������������������������, ������̂������������������~������������������������������������Where ������������������������ is the spot exchange rate of a given currency at time ������������ and ������������������������,������������ is the correspondingfundamental, in this case, the relative price ratio between the given currency and the United States. Bythe cointegrating relationship, as indicated, the estimated residuals ������̂������������������ will be I(0) and iid, The use of thisstationary residual term that results from regressions of the cointegrating relationship can provideadditional predictive power for changes in the spot rate. The specification of the VECM in the context of the hybrid theory model is as follows: ∆������������������������ = ������������ + ������������∆������������������������−1 + ������������∆������������������������−1 + ������������������������̂������������−1 + ������������������������The primary differences here, between both the cointegrating regression and hybrid specification are theinclude of lagged first differences of the exchange rate and relative price ratio and the inclusion of thefitted residuals from the cointegration regression. So, rather than forecasting spot exchange rates in levelterms, the VECM forecasts changes in the exchange rate. Of interest is the coefficient ������������ from the fitted60 InFER|2018 APRIL

The Role of Theory-Motivated Fundamentals in Long-Run Exchange Rate Forecastingresiduals—a negative, significant coefficient implies that there is a tendency for deviations from thecointegrating relationship to be “pulled” back to zero in the long-run. This intuition is complementaryto the specification of the hybrid model in the body of the analysis without cointegration elementsincluded.Figure 41: Modified Vector Error-Correction Model Regression OutputDependent Variable: Change in Bilateral Spot Exchange Rate (First Difference) Exchange Rate Series Swiss Franc British Pound Japanese YenLagged Exchange Rate 0.283*** 0.365*** 0.321*** (0.046) (0.043)(First Difference) (0.035)Lagged Relative Price -0.153 -0.074 -0.112Ratio (First Difference) (0.287) (0.124) (0.372)Lagged Fitted -0.021*** -0.032*** -0.032*** (0.012) (0.01)Cointegration Residual (0.008)Constant 0.002* -0.001 0.002 (0.001) (0.001) (0.002)Observations 532 532 364R2 0.089 0.145 0.128 HAC robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1From the regression output, there is overwhelming evidence of this error-correcting behavior in themodified hybrid model with first-differenced dependent and independent variables. In all regressions,the coefficient estimate for the cointegration residual (������������) is negative and statistically significant at the 99%level. Again, the negative coefficient lends support to the intuition that large deviations from thecointegrating relationship (i.e. when the spot exchange rate is far from the linear relationship with therelative price ratio) will be largely self-correcting in the long-run.9. Forward Market Analysis Results Given the methodology employed to conduct forecasts of exchange rates with the hybrid modelinvolves direct step-ahead forecasting, there are corresponding rates in the forward market from whichadditional predictive power may be ascertained. To further motivate this approach, it is appropriate tofirst illustrate the respective error series to get a sense of their relationship at first-pass. Recall the hybridmodel errors are those generated from the difference between the hybrid forecasting model and theactual exchange rate series, while the forward market errors are generated from the difference betweenthe forward rate transacted at the step-ahead horizon and the corresponding realized spot rate: 2018 APRIL|InFER 61

RESEARCH Figure 43: Forward Market & Hybrid Model Error Series (3-Month Ahead) Figure 42: Forward Market & Hybrid Model Error Series (1-Month Ahead) 0.2 0.1 0.15 0.05 0 0.1 -0.05 0.05 -0.1 0 Forward Market Errors -0.05 Hybrid Model Errors -0.1 Figure 44: Forward Market & Hybrid -0.15 Model Error Series (6-Month Ahead) 0.2 -0.2 0.1 -0.25 0Feb-97 -0.1May-98 -0.2 Aug-99 -0.3 Nov-00 -0.4 Feb-02 May-03 Forward Market ErrorsAug-04 Hybrid Model ErrorsNov-05 Feb-07 Figure 46: Forward Market & HybridMay-08 Model Error Series (2-Year Ahead)Aug-09 0.3 Nov-10 0.2 Feb-12 0.1 May-13 0 Aug-14 -0.1 Apr-97 -0.2 Jul-98 -0.3 Oct-99 -0.4 Jan-01 Apr-02 Forward Market Errors Jul-03 Hybrid Model Errors Oct-04 Jan-06 Apr-07 Jul-08 Oct-09 Jan-11 Apr-12 Jul-13 Oct-14 Forward Market Errors Hybrid Model Errors Figure 45: Forward Market & Hybrid Model Error Series (1-Year Ahead) 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4Jul-97 Oct-98 Jan-00 Apr-01 Jul-02 Oct-03 Jan-05 Apr-06 Jul-07 Oct-08 Jan-10 Apr-11 Jul-12 Oct-13 Jan-15 Jan-98 Mar-99 May-00 Jul-01 Sep-02 Nov-03 Jan-05 Mar-06 May-07 Jul-08 Sep-09 Nov-10 Jan-12 Mar-13 May-14 Forward Market Errors Hybrid Model Errors Figure 47: Forward Market & Hybrid Model Error Series (5-Year Ahead) 0.2 0.1 0 -0.1 -0.2 -0.3Apr-06 Dec-06 Aug-07 Apr-08 Dec-08 Aug-09 Apr-10 Dec-10 Aug-11 Apr-12 Dec-12 Aug-13 Apr-14 Dec-14 Apr-09 Sep-09 Feb-10 Jul-10 Dec-10 May-11 Oct-11 Mar-12 Aug-12 Jan-13 Jun-13 Nov-13 Apr-14 Sep-14 Feb-15 Forward Market Errors Hybrid Model Errors62 InFER|2018 APRIL

The Role of Theory-Motivated Fundamentals in Long-Run Exchange Rate ForecastingAgain, to empirically assess the degree to which information in the forward market can be used to predictthe errors of the hybrid forecast model above, I conduct forecast encompassing regressions of thefollowing specification: ������������������������,������������+������������ = ������������ + ������������������������������������������������,������������+������������ + ������������������������,������������+������������Where ������������������������,������������+������������ is the hybrid model forecast error series from the k-period ahead forecast for a givencurrency ������������ , and ������������������������,������������+������������ is the error series constructed from the differences between log spot exchange ratesat period k and the forward exchange rates established with information at time t to be transacted k-periods ahead. Regression results are as follows: Figure 48: Forward Market Forecast Encompassing Regressions - USD/GBP Exchange Rates Dependent Variable: Hybrid Model Forecast Errors, k-periods ahead Forecast Horizon 1-Month 3-Month 6-Month 1-Year 2-Year 5-YearForward Market 0.981*** 0.946*** 0.876*** 0.767*** 0.598*** -0.222***Exchange Rate Errors, (0.006) (0.02) (0.032) (0.044) (0.101) (0.071)k-periods aheadConstant 0.000 -0.001 -0.003 -0.007 -0.002 -0.049*** (0.000) (0.001) (0.003) (0.005) (0.016) (0.013)Observations 221 219 216 210 111 75R2 0.988 0.950 0.877 0.776 0.500 0.227 HAC robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1Conducting the analysis of the forward exchange rates per the forecast encompassing methodologyspecified above, I find that, in all horizons (1-month, 3-month, 6-month, 1-year, 3-year, and 5-yearforward rates), the errors from the forward market (with respect to the realized exchange rates to whichthey correspond) have a statistically significant relationship with the resulting errors of the forecastmodel. With all six forecast encompassing regressions, the forward errors are statistically significant atthe 99% level in prediction of the errors from the hybrid model. The magnitude of the coefficient isalways below 1, and decreases in magnitude as the forecast horizon increases, which is consistent with theresults from the hybrid model alone. Thus, at all horizons, forward exchange rates established with thesame information available for the construction of the hybrid forecast seem to contribute to thepredictive power of the hybrid model insofar as they can predict the errors of the hybrid model thatfollow. This provides evidence of a weakness in the hybrid forecasting model which can be improved byinclusion of the forward market in some capacity—since the errors of the hybrid model can be predictedas such, it can be improved. Determining how to do so is outside the scope of the research, and is left forfuture research. This effect is most pronounced with the 1-month ahead forward rates—the coefficient estimate forthe forward errors is 0.981 with an R2 of 0.988, suggesting there is significant explanatory power 2018 APRIL|InFER 63

RESEARCHembodied in the forward errors with respect to the errors from the hybrid model. At the 5-year aheadforecast horizon, however, the coefficient is statistically significant and negative—I do not have anexplanation, either theoretical or economic for this phenomenon and defer an explanation to furtherresearch on the subject. I would posit that at this horizon, given the deterioration of the hybrid modeland the large displacement implicit in the forecasts, forward or otherwise, could be to blame forunintuitive results such as this. It is also possible that the small sample size (only 75 months ofobservations are included in the actual regression) is also biasing results. While forwards for longer timehorizons exist, I have not included them in this analysis. It would be insightful to assess the broader trendof these forecast encompassing regressions at longer horizons. Broadly, however, despite the unintuitive result from the 5-year ahead forecast, the results from theforward market analysis suggest that that errors that result from forward exchange rates relative to therealized exchange rate they are forward against have significant, statistically robust predictive power withrespect to the errors from the hybrid theory model of interest in this analysis. Further research on thissubject would be helpful toward understanding how to directly incorporate this supposed predictivepower into more complex exchange rate forecasting models. Further, generalizing the results beyond theUSD/GBP exchange rate would be valuable for assessing the robustness of this contribution to changesin currency (i.e., with the additional exchange rate forecasts conducted in this analysis).10. Conclusion While the random walk model as popularized by Meese and Rogoff is likely the most accuratemodel for forecasting exchange rates in the short run, this analysis finds strong evidence to suggest thatthe inclusion of an underlying fundamental like purchasing power parity can improve on this simplisticapproach, particularly in the long-run. Using an adapted specification of the hybrid model firstpostulated in Mark (1995), this analysis finds that theory, in the form of purchasing power parity, hasboth a statistically and economically significant role contributing predictive power to forecasts of anumber of bilateral exchange rates, at both the monthly and annual frequency. Furthermore, thecontribution becomes more economically significant as the time horizon expands. In this context, therandom walk serves as a foil to the fundamental—as the contribution of purchasing power parityincreases over displacements in time, the contribution of the past realizations of the exchange ratediminishes, though it remains statistically significant and nontrivial in magnitude. These results are largely robust to the choice of country-specific bilateral exchange rate, asdemonstrated through forecasts conducted on USD/CAD, USD/CHF, USD/JPY, and USD/GBPbilateral exchange rates at the monthly-frequency up to 5-years ahead. This analysis serves as acontribution to the work of Mark (1995) and others in this vein by expanding upon the existingframework with additional observations that include the financial crisis. Of note in this analysis, beyondthe analysis at the monthly-frequency, I conduct long-run forecasts of dollar-sterling exchange rates withthe Bank of England dataset. Results from these forecasts lend further credibility to the use of the64 InFER|2018 APRIL

The Role of Theory-Motivated Fundamentals in Long-Run Exchange Rate Forecastingpurchasing power parity fundamental with a much broader dataset and at longer horizons—however, Ido find that the quality of the forecasts deteriorate beyond the 5- to 6-year forecast horizon used at themonthly frequency. Further, there are challenges associated with conducting forecasts on a sample of data that spans somany broad global events, institutions and exchange rate regimes. To assess the robustness of theforecasts and fundamental to changes in underlying institutions, I subdivide the dataset and conductforecasts with the hybrid specification. Results from these forecasts are dramatically different from thoseconducted on the full sample and dramatically different from one another—despite the degree to whichpurchasing power parity can be considered a fundamental to which the deviations in exchange rate self-correct, this research suggests that the fundamental is highly sensitive to changes in underlyinginstitutional assumptions. While the coefficients for the theory and past components provide sufficient evidence to reject thepredominance of the random walk for exchange rate forecasting at medium- and long-run forecasthorizons, I defer to conventional measures of forecast evaluation and explanatory power to more broadlyassess the quality of the forecasts at each horizon. Regarding model fit and accuracy, plots of R2 andRMSE suggest that there is an inherent trade-off between the accuracy of the model and the quality ofthe model as the forecast horizon increases. While the country-specific evolution of these metrics varies,the general trend borne out in the data is decreasing R2 with the forecast horizon and increasing RMSE.Broadly this implies that the quality of the forecast deteriorates as the forecast horizon increases, despitethe continued contribution of purchasing power parity at these horizons. In some instances, this pattern seems to stabilize somewhat throughout the forecasts, and does notsuggest the trend will continue indefinitely (in the case of the Swiss franc, Japanese yen and poundsterling at the monthly frequency) and other instances that seem to suggest the deterioration continueswell beyond the forecast horizon analyzed (annual pound sterling and the Canadian dollar). As indicated,I see this as a reflection of the inherent challenge in forecasting a highly volatile series such as exchangerates at exceptionally long-run forecast horizons—despite this deterioration in overall forecast quality, Iam confident that the inclusion of the purchasing power parity theory component improves theforecasts relative to the alternative of, say, the random walk or univariate autoregressive model. To empirically evaluate this claim, I test the forecast accuracy of the hybrid theory model againstthat of a univariate autoregressive model that excludes the possible role of the fundamental inconducting the forecasts. In terms of explanatory power (measured with R2) and model fit (measuredwith RMSE and AIC), the hybrid theory model improves upon the more parsimonious autoregressivemodel as soon as the 1-month ahead forecast horizon, but not relative to the forward rate. Since R2 would,by construction, be higher with the inclusion of an additional regressor, a more robust test of forecastaccuracy is in order. In this spirit, I conduct Diebold Mariano tests for all forecasts to determine whetherthe difference in squared forecast error between the two models is statistically significant. Except for the 2018 APRIL|InFER 65

RESEARCHGold Standard subperiod, I find statistically significant evidence of an improvement in accuracy withthe use of the hybrid theory model. Generally, in the monthly frequency forecasts, this occursapproximately 1-year ahead in terms of forecast horizon. Beyond direct evaluation per this methodology, I extend the analysis to the forward exchange ratemarket to determine whether there is economically valuable predictive content implicit in the errorsfrom the forward rates. To test this assumption, I create residual series for both the hybrid forecasts andfrom the difference between the forward rate and realized spot rate, and then conduct forecastencompassing regressions to assess the predictive power of the forward errors relative to the forecasterrors. I find that, for the pound sterling exchange rates, there is statistically and economically significantpredictive power contained in forward rates toward the end of explaining the errors of the hybrid model.More research is needed to directly incorporate this contribution into more complex, theory-basedexchange rate forecasting models. In the spirit of additional research, this analysis is somewhat limited in scope—there are boundlessopportunities to apply this hybrid model to a battery of other exchange rates and price data, as well as toapply other indicators in the theory component (such as the Taylor Rule variables from other researchdescribed above. Beyond an analysis of other countries in the current framework, the historical analysisof the dollar-sterling exchange rates is insightful for understanding the scope of (and limitations of) therole of a fundamental across institutions. Naturally, an analysis of this nature would be limited by theavailability of data. More tangibly, perhaps, a more expansive analysis on the forecast encompassingregressions from the forward market would be valuable—since it is not the predominant focus of thisresearch, the analysis is somewhat terse. One key limitation I recognize in this analysis deserving of further attention is the comparison ofthe hybrid model to some baseline. I conclude that the inclusion of the lagged exchange rate in thespecification provides sufficient evidence of the improvement upon the random walk whenincorporating the theory element directly in the specification. However, a direct comparison against aconstructed random walk series (in terms of forecast evaluation metrics) would be useful for morerobustly assessing the predictive power the hybrid model provides in excess of a simple random walk. One additional limitation worth addressing is the underlying assumptions of the choice offundamental. In this use of the “fundamental exchange rate” is the implicit assumption that purchasingpower parity is an appropriate theoretical underpinning for exchange rate forecasting in the hybridmodel context. There are important historical limitations that deserve our attention if we are to continuein this vein. Purchasing power parity as we understand it was first introduced in 1918 by Gustav Cassel.As such, there are approximately 60 years of observations for price levels that pre-date the purchasingpower parity model. The question that arises, then, is whether a model developed in the 20th centurycan appropriately describe data from the 19th century.66 InFER|2018 APRIL

The Role of Theory-Motivated Fundamentals in Long-Run Exchange Rate Forecasting I would contend that purchasing power parity is substantiated with appropriate precedent towarrant the use in this context, and is powerful enough that it can be used to describe data prior to itsinception. However, the issue of assuming a single “fundamental exchange rate” as described above isagain called into question. If purchasing power parity is not appropriate in this context, an alternativemust be provided which could be borne out from the existing literature (Taylor Rule coefficients, forinstance). If there is an alternative structural model employed prior to the start of our sample, we mightcompare its relevancy to the use of purchasing power parity. I am not sure if such a model exists and, assuch, this issue is deserving of further study.11. Appendix – Selected Graphicsβk βk Figure A1: Evolution of Coefficients for USD/GBP Forecasts - Full Bank of England 12 Dataset Sample, 1861-2015 - HAC Error Bars Lagged USD/GBP XR P/P* 1.2 1 0.8 0.6 0.4 0.2 0 0 2 4 6 8 10 k-lags Figure A2: Evolution of Coefficients for USD/GBP Forecasts - Gold Standard, 1861-1939 - 12 HAC Error Bars Lagged USD/GBP XR P/P* 1 0.8 0.6 0.4 0.2 0 0 2 4 6 8 10 -0.2 -0.4 k-lags 2018 APRIL|InFER 67

RESEARCHβk βk Figure A3: Evolution of Coefficients for USD/GBP Forecasts - Bretton Woods Era - 1944- 12 1973 - HAC Error Bars Lagged USD/GBP XR P/P* 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 -0.2 0 2 4 6 8 10 -0.4 -0.6 -0.8 k-lags Figure A4: Evolution of Coefficients for USD/GBP Forecasts - Current Float - 1974-2015 - 12 HAC Error Bars Lagged USD/GBP XR P/P* 1.4 1.2 1 0.8 0.6 0.4 0.2 0 -0.2 0 2 4 6 8 10 -0.4 -0.6 -0.8 -1 k-lags68 InFER|2018 APRIL

The Role of Theory-Motivated Fundamentals in Long-Run Exchange Rate Forecasting12. ReferencesAbhyankar, Abhay, Lucio Sarno, and Giorgio Valente. 2005. \"Exchange rates and fundamentals: evidence on the economic value of predictability.\" Journal of International Economics (Elsevier Science B.V.) 66: 325-348.Boothe, Paul, and Debra Glassman. 1987. \"Off the Mark: Lessons for Exchange Rate Modelling.\" Oxford Economic Papers (Oxford University Press) 39 (3): 443-457.Burns, Kelly, and I. Moosa. 2012. \"Can exchange rate models outperform the random walk? Magnitude direction and profitability as criteria.\" Economia Internazionale 65 (3): 473-490.Choi, Doo-Yull, and Nelson, C. Mark. 1997. \"Real exchange-rate prediction over long horizons.\" Journal of International Economics (Elsevier Science B.V.) 43: 29-60.Christoffersen, P.F., and F.X. Diebold. 1998. \"Cointegration and Long-Horizon Forecasting.\" Journal of Business and Economic Statistics 16 (4): 450-458.Diebold, Francis X. 2006. Elements of Forecasting. 4th. South-Western College Publishers.Dimsdale, N., and R. Thomas. 2016. \"Three Centuries of Data - Version 2.3.\" Bank of England. Accessed May 24, 2017. http://www.bankofengland.co.uk/research/Pages/onebank/threecenturies.aspx.Engel, Charles, Nelson C Mark, and Kenneth D West. 2012. \"Factor Model Forecasts of Exchange Rates.\" NBER Working Paper Series (NBER) 1-20.Engel, Charles, Nelson C Mark, and Kenneth D. West. 2007. \"Exchange Rate Models Are Not As Bad As You Think.\" In NBER Macro Economics Annual 2007, Volume 22, edited by Daron Acemoglu, Kenneth Rogoff and Michael Woodford, 381-441. Chicago: University of Chicago Press.Grossmann, Axel, and Marc W. Simpson. 2011. \"Can a relative purchasing power parity-based model outperform a random walk in forecasting short-term exchange rates?\" International Journal of Finance & Economics 16 (4): 375-392.Grossmann, Axel, and Marc W. Simpson. 2010. \"Forecasting the Yen/U.S. Dollar exchange rate: Empirical evidence from a capital enhanced relative PPP-based model.\" Journal of Asian Economics (Elsevier Science B.V.) 21 (5): 476-484.Leitch, Gordon, and J. Ernest Tanner. 1991. \"Economic Forecast Evaluation: Profits Versus the Conventional Error Measures.\" The American Economic Review (The American Economic Association) 81 (3): 580-590. 2018 APRIL|InFER 69

RESEARCHLothian, James R. 1991. \"A History of Yen Exchange Rates.\" Japanese Financial Market Research (Elsevier Science B.V.) 1-22.Lothian, James R., and Mark P. Taylor. 1996. \"Real Exchange Rate Behavior: The Recent Float from the Perspective of the Past Two Centuries.\" Journal of Political Economy (The University of Chicago Press) 104 (3): 488-509.—. n.d. \"Two Hundred Years of Sterling Exchange Rates and the Current Float.\" London: Irish Management Institute Centre for Economic Policy Research.MacDonald, Ronald, and Ian W. Marsh. 1997. \"On Fundamentals and Exchange Rates: A Casselian Perspective.\" Review of Economics and Statistics 79 (4): 655-664.Mark, Nelson C. 1995. \"Exchange Rates and Fundamentals: Evidence on Long-Horizon Predictability.\" American Economic Review 85 (1): 201-218.Meese, Richard A, and Kenneth Rogoff. 1983. \"Empirical Exchange Rate Models of the Seventies: Do they fit out of sample?\" Journal of International Economics (North-Holland Publishing Company) 14: 3-24.Meese, Richard, and Kenneth Rogoff. 1988. \"Was it Real? The Exchange Rate-Interest Differential Relation OVer the Modern Floating-Rate Period.\" The Journal of Finance (Wiley for the American Finance Association) 43 (4): 933-948.Papell, David H., and Tanya Molodtsova. 2009. \"Out-of-sample exchange rate predictability with Taylor rule fundamentals.\" Journal of International Economics (Elsevier Science B.V.) 77: 167- 180.Taylor, Alan M. 2002. \"A Century of Purchasing-Power Parity.\" Review of Economics and Statistics 84 (1): 139-150.70 InFER|2018 APRIL

The Role of Theory-Motivated Fundamentals in Long-Run Exchange Rate ForecastingMonetary Policy and its Effecton Inequality: The Role ofUnconventional Monetary PolicyMeghan Greene and Medha NairAdvisor: Dr. Jaime Marquez and Dr. Cristino Arroyo (Johns Hopkins SAIS)The Research Paper is submitted in partial fulfillment of the requirements for theMaster of Arts degree in International Economics and FinanceThe Johns Hopkins UniversitySchool for Advanced International Studies (SAIS)Washington, D.C.Abstract:Our research, seeks to analyze the extent to which monetary policy effects income inequality in Canada,the United Kingdom and the United States. Much of the existing literature either emphasizes theempirical associations between various proximate determinants of income inequality withoutincorporating monetary policy to this analysis or alternatively, addresses the theoretical linkagesbetween monetary policy and income inequality while failing to assay them to the rigor of econometricanalysis. Unlike much of the existing literature, we recognize econometric properties and empiricallyanalyze these aforementioned theoretical findings taking into account monetary policy. We begin byproposing a bivariate model, which evolves to take the forms of a time series-based model, theory-basedmodel as well as a multi-equation dynamic model, respectively. Our findings, across models suggestthat there is no strong evidence in favor of the argument that monetary policy, particularly quantitativeeasing, has increased the level of income inequality observed in the industrialized countries of ourstudy.Key words: income inequality, monetary policy, Gini coefficient, unconventional monetary policy 2018 APRIL|InFER 71

RESEARCH1. Motivation The word ‘inequality’ has a myriad of meanings. Certain schools of development theory defineinequality as the lack of economic opportunity for a certain section of the population. As economicopportunities are inaccessible to some, this forms the root cause of all other types of inequalities- be itsocial or political. On the other hand, there exists an alternative school of thought that defines inequality as simplythe income gap between the sections of the society, or in other words, an unequal distribution ofwealth. This theory emphasizes a social paradigm that creates an impetus for the accumulation ofwealth in the hands of a few, thus, intensifying the wedge between the rich and the poor (Alvaredo etal., 2013). Social and moral reasons aside, the increasing income inequality in most parts of the world iscapturing attention for purely economic reasons as well. For an economy to prosper, it is imperativethat the consumption capacity of the economy remains at a level that can sustain economic growth. Most developed countries have seen a rise in inequality, especially after the 2008 financial crisis,as can be illustrated in the graph of the Gini coefficients below for Canada, the United Kingdom, andthe United States. As most governments scrambled to put together policies that would prop theeconomy back to its feet, a crucial element of the recovery plan was ignored as a potential cause forworsening inequality: the bail out packages. The US government instituted a 3 trillion dollar packageto bail out major banks involved in the crisis. This involved a significant transfer of income into thehands of those who already belonged to the top one percent of income earners of the economy(Piketty and Saez, 2003). For economists, such transfers are interesting due to potential consumptiondistortions these transfers would have on the economy’s growth prospects. Based on the consumptionfunction, the marginal propensity to consume for individuals belonging to lower income levels ismuch higher than the marginal propensity to consume of individuals belonging to higher incomelevels. This means that it is more probable that a low income individual would spend/consume a $1transfer of money, while a high income individual would have a greater propensity to save the $1transfer. Analogously, if we extend this inference, we could say that a low income individual is likelyto derive greater utility out of a $1 transfer than a high income individual. Therefore, not only is this“new era” of monetary policy interesting for its effects on income inequality but also in a world wherethe post-recession recovery has yet to be fully accomplished and where aggregate demand has yet toreturn to pre-crisis levels. For these reasons, we find it imperative to address and investigate the increase in incomeinequality in the developed world in the wake of the shift in monetary policy following the globalfinancial crisis.72 InFER|2018 APRIL

Monetary Policy and its Effect on Inequality: The Role of Unconventional Monetary Policy Figure 1: Gini Coefficients of the US, the UK and Canada.52.48.44.40.36.32.28.24 1985 1990 1995 2000 2005 2010 19802. Key Papers and Findings Discussion about the relationship between income inequality and monetary policy is taking-on amore central role in policy debates in the United States, particularly in response to the handling of thefinancial crisis during which the Central Bank accommodated the financial sector but not necessarilyevery-day borrowers and lenders. “...As the American economy begins to improve, influential peoplein the financial sector will continue to talk about the need for a prolonged period of low interest rates.The Fed will listen” (Acemoglu and Johnson, 2012). The result: rising inequality. Some argue that, byenforcing unconventional monetary policy or Quantitative Easing (QE), the United States FederalReserve allegedly contributed to the increase of income inequality in the country. However, the debatesurrounding the effects of monetary policy on income inequality in the United States has not yetreached a conclusion. In the past, quantitative easing (QE) has enabled the Fed to cut interest ratesuntil the Lower ZeroBound. Then to ease the burden of financial distress on the markets, the Fed bought the high risk bondsfor trillions of dollars in value; hoping to stimulate investment only to result in a decrease inunemployment. Josh Bivens strongly supports this claim that expansionary monetary policy reducesinequality. Bivens (2014) states that the most important distributional effect of expansionary monetarypolicy is by far the impact that lower unemployment rates have on wages at the bottom and middle ofthe wage distribution. Opponents of Bivens’ argument --like Kevin Warsh who criticized QE on publictelevision by calling it a ‘reverse Robin Hood policy’, speaks for those who believe QE is only amediocre mean to remedy the shortcomings of the economy during the crisis because only investors orany individual who had access to credit, benefit (Warsh, MarketWatch, 2014). Otherwise said, suchinvestors benefited more from the QE than the rest of the suffering economy, resulting in an increase inthe income distributionimbalance. 2018 APRIL|InFER 73

RESEARCH Coibion et al. highlight the lack of consensus on the link between inequality and monetary policyby recognizing the more-typical channels that are discussed in the literature: globalization, skill-biasedtechnological advances, unionization and labor market rigidities, etc. while also discussing the channelsthrough which monetary policy and inequality may be linked (2012). These channels includeheterogeneity in the composition of household income, level of participation in the financial sector, the“portfolio channel,” among others. Their groundbreaking research finds that for the United States, “acontractionary monetary policy shock raises the observed inequality across households in income, laborearnings, expenditures and consumption” (2012). Furthermore, Romer and Romer argue that “theaverage income of the poor tends to be lower in countries where monetary policy has produced higheraverage inflation and greater macroeconomic volatility” (1998). There is some evidence that suggeststhat Federal Reserve policy -- specifically Quantitative Easing-- has had an impact on the real yieldearned by credit market participants, however less evidence indicates the directional effect this has hadon inequality. For example, it has been argued that higher income individuals tend to be active incapital markets and hold assets. To the extent that QE has increased the value of these assets, inequalitywould increase as a result. Saiki and Frost utilize a vector autoregressive model and find empiricalevidence to support this claim for the case of Japan over the past decade: “unconventional monetarypolicy widened income inequality, especially after 2008 when quantitative easing became moreaggressive … largely due to the portfolio channel” (Saiki et al., 2014). On the other hand, some argue both the middle class and upper class in society tend to hold assets.This could reduce some between-class inequality. Furthermore, economists argue that monetary policyis neutral in the long-run and therefore changes in monetary policy can only temporarily impact real-side issues such as inequality. Ultimately, due to the lack of consensus, the heated debates about thelevel of inequality that currently exists (and has been increasing since the 1980s) in the United Statesand other industrialized countries, further research such as this is important in order to understand theimplications of policy decisions made by the United States and other industrialized countries that haveimplemented Quantitative Easing and have engaged more generally in unconventional monetary policy. In addition to simple Quantitative Easing, questions have been raised about aggregate investment(government expenditure) skewing the overall income distribution. Deininger and Squire (1998) assertthat inequality in asset holdings like land places downward pressure on growth prospects particularlyfor poorer populations within country. A key motivation driving this work is the Kuznets’ curve andwhether or not its relationship is empirically substantiated – for which the authors find little evidencein favor. On the other hand, Deininger et al. (1998) find that poorer quintiles of the population benefitrelatively more from aggregate investment and from the creation of new assets (investment) rather thanredistributionof existing assets. Economists argue that trade liberalization and the openness of an economy can play a pivotal rolein effecting income inequality. Fischer (2001) documents the results of trade liberalization andassociated economic changes on an economy particularly in relation to inequality. Fischer finds that “inthe long run, increases in the wage to wealth ratio are captured by reductions in the interest rate. Hencea fall in the long run interest rate leads to less inequality in the steady state” (pp. 557). Furthermore,74 InFER|2018 APRIL

Monetary Policy and its Effect on Inequality: The Role of Unconventional Monetary PolicyFischer finds that based on the model constructed, trade liberalizations can actually reduce inequalityacross the dynamic and time-profile of the labor-abundant country. On the other hand, land-abundant(capital) countries experience the opposite and inequality increases post liberalization in the short andmedium terms. However, these adverse effects for the land-abundant country can be mitigated withnearly perfectcapital mobility (2001). Furthermore, the majority of the aforementioned research focuses on inequality assessed at themacro level, inequality at the household-level (a more micro-understanding) would require a moredetailed study of expenditure and saving patterns at the individual level. The paper published byChowdhary (2010) is a key contribution to this research in the way that it achieves a similar outcome asother works but at the micro level. While the life cycle hypothesis1 and the study of individualbehaviors in relation to spending and savings may provide an insight into how inequality may be a self-implicative process2, we believe that one of the major influencers of household level inequality could bethe access to credit. As Chowdhary states: “access to credit has a significant negative impact on theinequality in the society as it negatively determines the log mean deviation of per capita consumptionexpenditures of households” –i.e. increased access to credit reduces poverty. However, the post crisisera (post 2008) has shown that there has been an improvement in the access to credit across incomequintiles in the United States, but what most people fail to recognize is the type of credit people haveaccess to and, most importantly, if this loan can be paid back without effecting the income inequalitydynamics. For instance, low income individuals have access to so-called “pay day loans”. These arepaycheck to paycheck loans and can be paid back with the receipt of the individual’s future paycheck.However, the interest rates on these short term loans average at about 300%) (Diagne et al, 2014). Moreoften than not, at these interest rates, the loans almost never get paid back, thereby reinforcing a systemof perpetual indebtedness for the individual. The fact that the demography of the recipients of theseloans generally include low income individuals further intensifies the problem. This theory findssupport in the paper by Fischer, Huerta, and Valenzuela (2010) where their findings suggest that theGini is positively associated with private credit and the more constrained the country despite higherlevels of inequality, the lower the level share of private credit. Therefore, it is not surprising that in anage of increased access to credit, we maystill observe soaring income inequality. Historically, economists have focused primarily on skill-biased technological change, increasedglobal trade, labor market institutions (unionization) as major contributing factors to incomeinequality as a result of monetary policy, rather than focusing on expansionary monetary policy. Oliver,Yuriy and Lorenz (2012) claim that the following existing channels- income composition channels,portfolio channels, financial segmentation channels, savings redistribution channels and1 The life-cycle hypothesis refers to the intertemporal consumption smoothing decisions or saving behaviors across their life-span.2 Due to financial constraints, it is possible to associate lower levels of saving with lower-income individuals due to differentpropensities to save and consume based on socio-economic status. Therefore, if this holds, by failing to save, lower-incomeindividuals may find themselves in an inequality trap. 2018 APRIL|InFER 75

RESEARCHearnings heterogeneity channels- all show ambiguous results (the last two have opposing effects). As aresult they turn to how monetary policy has effected consumption based on historical consumptionand expenditure data. The paper studies the contribution of monetary policy shocks to consumptionand income inequality in the US since the 1980s. Contractionary monetary policy actions systematicallyincrease inequality in labor earnings, total income, consumption and total expenditures. Furthermore,monetary shocks can account for a significant component of the historical cyclical variation in incomeand consumptioninequality. As we have seen above, there exists a wealth of research that has made an attempt to investigatethe various aspects of income inequality. However, a very small amount of the research is dedicated tostudying monetary policy as an instrument that exacerbates inequality among the masses. The paper byKunt and Levine (2009) critically reviews the literature on inequality, highlighting substantive gaps inthe literature. First, there is also startlingly little research on how formal financial sector policies---suchas bank regulations or securities markets laws---affect inequality. Given the accumulated body oftheoretical and empirical research on the central---though frequently underappreciated---role of financein explaining economic inequality, this is serious gap. In addition, given the enormous welfareimplications at stake, there are potentially high returns to theoretical and empirical research on theimpact of financial regulations on economic opportunity, the intergenerational persistence of relativeincomes, and the distribution of income. Second, many theories motivate redistributive policies as amechanism for de- linking an individual’s opportunities from parental wealth. Financial developmentsthat expand individual economic opportunity create positive, not negative, incentive effects, and theyavoid the adverse repercussions associated with attempts to equalize outcomes (Kunt et al, 2009).Financial development boosts both efficiency and the equality of opportunity. In light of these drawbacks, it is imperative to clarify the contribution of our paper to the existingwealth of inequality literature. This paper seeks to understand and develop the variables that aresignificantly known to effect inequality. To put it briefly, we use time series data for the variables andassess their effects on the Gini Coefficient. In the end, this paper does not seek to bridge the gaps in theexisting literature, but to simply add to the abundance of its existence, analyzing areas that are notwidely researched at this time – namely incorporating the role of monetary policy to models thatcontrol forother important factors while also incorporating analysis of time-seriescharacteristics.3. Methodology As reported in the literature review, one of the major value adds of this research is the detailedanalysis of the time series properties of the components used to estimate inequality in the United States,the United Kingdom and Canada. Based on previous literature, the variables utilized in this model topredict income inequality (as measured by the Gini coefficient) are government expenditure (as a wayto capture fiscal expenditure and investment – calculated as nondefense expenditure as a share ofGDP), trade openness (total trade as a percentage of GDP), unemployment, and a measure of skill-biased technological change (GDP per capita per hour worked adjusted for inflation). In addition, inorder to understand the role of monetary policy in estimating inequality in the countries of study, we76 InFER|2018 APRIL

Monetary Policy and its Effect on Inequality: The Role of Unconventional Monetary Policyutilize the respective real long-term interest rates, and money base as a share of GDP. The United States, the United Kingdom and Canada were chosen as cases of interest in order tocapture a potential deviation in inequality outcomes related to differences in the use of unconventionalmonetary policy. The United States and the United Kingdom both engaged in Quantitative Easingwhile Canada did not. Should we see strong deviations in the evolution of the measures of inequalityfor the respective countries, it may be related to this policy shift. Furthermore, these countries sharesimilar levels of global integration with respect to international trade and access to capital marketswhich provides a level of initial consistency in the chosen countries.What are we considering monetary policy? Figure 2: Money Base as percent of GDP in the US, the UK and Canada As briefly discussed in the motivation and introduction, there are various documented channelsthrough which monetary policy may impact inequality. The channel that we emphasize is through themoney base (through QE). The growth in the money base may have an impact on inequality throughinflation. Inflation could be linked to inequality because of its relation to the real money holdings ofsocietal members as well as its relationship to borrowing and lending through the interest rate. If, forexample, individuals were to engage in long-term borrowing and the inflation rate were to increasehigher than the interest rate, the debtor is essentially receiving a transfer from the creditor, whichtherefore would decrease inequality (assuming the borrower is relatively poorer than the lender).Furthermore, and related, assuming that the majority of low income individuals in a country hold themajority of their wealth in cash whereas high income individuals tend to hold the majority of theirwealth under other financial mechanisms, inflation would decrease the purchasing power of poorerindividuals, – while also potentially increasing the wealth of asset-holding high-income individuals – 2018 APRIL|InFER 77

RESEARCHultimately increasing inequality. This generates some tension with the initially mentioned channel i.e.inflation reduces the purchasing power of lower-income cash-holders while simultaneously facilitatinga transfer from creditors to borrowers, not to mention its effect on increasing asset prices (likelyincreasing inequality). Therefore, the role of the money base in affecting inflation is an empirical issuedue to these juxtaposed forces. The below graphs illustrate one of these phenomena (inflation and the interest rate). The seriesrepresents the inflation rate minus the long term interest rate. It can be noted that over the past 16 years(since the turn of the century), the two rates have been converging across the countries of the sample.Although the differenced series has only slightly and inconsistently moved into the positive regionsince 1990 in the US and Canada, this suggests that a transfer occurred from the creditor to the debtor,which could reduce observed inequality. Figure 3a: US Inflation minus LT Interest Rate 4.00 2.00 0.00 -2.00 -4.00 -6.00 -8.00-10.00 Figure 3b: Canada Inflation minus LT Interest Rate1.000.00-1.00-2.00-3.00-4.00-5.00-6.00-7.00-8.00-9.0078 InFER|2018 APRIL

Monetary Policy and its Effect on Inequality: The Role of Unconventional Monetary Policy 8.00 Figure 3c: UK Inflation minus LT Interest Rate 6.00 4.00 1982 1987 1992 1997 2002 2007 2012 2.00 0.00 -2.001977 -4.00 -6.00 -8.00-10.00A. Any priori evidence of the effect of monetary policy on income inequality? As a first measure of the evolution of inequality and its relationship to the Global Financial Crisisand therefore the unconventional monetary policies that followed, key time series analyses wereconducted on the three Gini coefficient series (for the United States, the United Kingdom and Canada).Based on simple correlograms, it was apparent that the three series were consistent with a one-lagautoregressive process. Running the three AR(1) models and obtaining the Durbin-Watson statisticslead to the conclusion that the models are not consistent with serially correlated error terms (Durbin-Watson statistics between 1.5 and 2). Therefore, we forecasted simple autoregressive models of each ofthe three Gini coefficient series. In order to explicitly observe its association with potential changes thatfollowed 2008, we split the sample into “pre-” (1977-2005) and “post-” (2006-2013) financial crisis. Themodels were estimated for the “pre” sample and then extrapolated through the post-period usingmulti-step forecasts. This will allow us to observe if the evolution of income inequality in the threecountries of study significantly differ from what would have occurred if unconventional policies wereto never have been implemented i.e. we can explore the counter-factual. If, for example, quantitativeeasing following the financial crisis increased income inequality, the observed Gini coefficient based onthe sample that excludes this period (1977- 2005) would be flatter than the actual observed datathrough the end of the sample. Furthermore, along these lines, it is informative to observe the underlying trends across the timesample in order to determine if or in what direction the trends have evolved between the first andsecond half of the sample (a true half-split, 1977-1995 and 1996-2013). If, for example, the underlyingtrend observed for the Gini coefficient were to steepen across the second half of the sample, then thiswould suggest that inequality is increasing across the sample regardless of the monetary policytransition. It will be useful to compare these trends to the forecasts predicted from the dynamic modelin order to determine where and how the differences arise between estimation-based and observationalfindings. In addition, in order to observe the effects of monetary policy on income inequality empirically, asimple autoregressive model of the Gini coefficient and the money base was run for each of the 2018 APRIL|InFER 79

RESEARCHindividual country-cases. If, as some argue, unconventional monetary policy is the driving force behindan increase in inequality observed following the financial crisis in countries that implementedquantitative easing, then we would expect to find a positive and significant coefficient on both thecontemporaneous and lagged observation of the money base3.B. Modeling of the Gini Coefficient: We continued by utilizing published research on the effect of monetary policy on incomeinequality (Gini) or more generally variables that have been found to be statistically significantlyassociated with the evolution of the Gini coefficient. We maintain a focus at the macro-level ratherthan for example the industry-level, due to data-availability as well as the common-practice indevelopment literature of using the Gini coefficient as an indicator of inequality. This led to threevariant models of the Gini coefficient: a model that adheres to the time-series properties (BalancedAutoregressive Distributed Lag) of the variables in the model, one that follows with theory’ssuggestions (Theory-Based Model), and finally a model built on the Saiki and Frost (2014) researchwith which they find a statistically significant association between monetary policy and incomeinequality for the case of Japan utilizing a Vector Autoregressive model (VAR). The variables takenfrom the survey of literature to be utilized in our modeling in some varying form are: labor income,total income, unemployment, inflation, interest rates, government expenditure (social spending), andtrade openness. Because of the high persistence found in these simple autoregressive models of the Gini coefficient,each of the series were examined for characteristics that are consistent with a unit root process in orderto determine the stationarity and validity of the model we utilize in this research. The findings for eachcountry suggest that many of the components of the model in this research are consistent with a unitroot process but are first-differenced stationary. Table 4: Stationarity of Variables for the US, the UK and CanadaUSA Stationary First-Differenced StationaryGini FTR (0.77) ✓(0.00)Gov’t Expenditure ✓(0.009) -Openness FTR (0.84)Unemployment ✓(0.04) ✓(0.00)Labor Productivity FTR (0.97) -Real LT Interest Rt. FTR (0.87)Money Base FTR (0.84) ✓(0.01) ✓(0.00)Canada Stationary ✓(0.0004)Gini FTR (0.39) First-Differenced StationaryGov’t ExpenditureOpenness ✓(0.02) ✓(0.00)UnemploymentLabor Income FTR (0.52) -Real LT Interest Rt. ✓(0.08) ✓(0.00)Money Base FTR (0.99) FTR (0.77) - FTR (0.65) ✓(0.00) ✓(0.00) ✓(0.003)3 The contemporaneous value is denoted as the first-lag because of the time in which the money base is calculated (end of theyear) such that changes in the money base are associated with changes in the other variables included (predominantly theGini coefficient) in a timelymanner.80 InFER|2018 APRIL

Monetary Policy and its Effect on Inequality: The Role of Unconventional Monetary PolicyUnited Kingdom Stationary First-Differenced StationaryGini FTR (0.57) ✓(0.07) ✓(0.09) -Gov’t ExpenditureOpenness FTR (0.76) ✓(0.0)Unemployment ✓(0.06) -Labor Income FTR (0.51)Real LT Interest Rt. FTR (0.18) ✓(0.0)Money Base FTR (0.93) ✓(0.0) ✓(0.01) Therefore, based on the above findings, the following model was formulated in order to generatea balanced equation that accounts for these time-series characteristics:log gt = α0 + α1 log gt-1 + α2 log lprodt + α3 log lprodt-1 + α4MBt-1 + α5MBt-2 + α6 tradesht +α7tradesht-1 + α8 Rltt + α9 Rltt-1 + εtThe second model is derived from the literature overview as discussed above and takes theform:log gt = α0 + α1 log gt-1 + α2 log lprodt + α3MBt-1 + α4 unemt + α5 gexpsht + α6 tradesht + εt It would be expected that increases in labor income would either increase income inequality if itwere to represents skill-biased changes, or decrease inequality if it were to represent changes across theboard. If quantitative easing benefited the wealthier individuals more than the lower-incomepopulation (via e.g. increase in asset prices) then the coefficient would be expected to be positive andsignificant. Increases in unemployment would be expected to increase income inequality in theobserved countries because as more individuals are out of work, the distribution of income across thepopulation would deteriorate. On the other hand, government expenditure (non-defense expenditure;e.g. unemployment benefits, education, etc.) should decrease income inequality if applied effectively.Lastly, the literature on trade openness is rather inconclusive in its effect on issues associated withincome inequality(unemployment, structure of the economy, skill-biased changes, etc.).The final model follows the Saiki and Frost (2014) methodology which is characterized as:Yt = [log(GDPt), πt, log(MBt), log(stock pricet), Ginit] This model controls for the portfolio channel of monetary policy, by including stock prices, inaddition to the traditional proxy for monetary policy (monetary base) that is utilized throughout thisresearch. Saiki and Frost (2014) produce statistically significant results suggesting that monetary policyhas increased income inequality for Japan. The results from this final methodology, perhaps the mostcomplex of our models, will be illustrated through orthagonalized impulse response functions –ordered in accordance to the Saiki and Frost model – i.e. log GDP, inflation, log monetary base, logstock price, and finallythe Gini coefficient. From these results, we will be able to better understand the association between incomeinequality and unconventional monetary policy and the robustness to our findings controlling for timeseries characteristics, moderating factors and covariates, and through a multi-equation VAR. 2018 APRIL|InFER 81

RESEARCH4. FindingsA. Initial Autoregressive Forecasts:Figure 5: Actual and Forecasted Gini Coefficients for Canada, the UK and the US .45.44.43.42.41.40.39.38.37.36 1985 1990 1995 2000 2005 2010 1980 Canada AR Gini Forecast Canada Gini.38.36.34.32.30.28.26 1985 1990 1995 2000 2005 2010 1980 UK AR Gini Forecast UK Gini82 InFER|2018 APRIL

Monetary Policy and its Effect on Inequality: The Role of Unconventional Monetary Policy.48.47.46.45.44.43.42.41.40 1985 1990 1995 2000 2005 2010 1980 US AR Gini Forecast US Gini For the above graphs, the following can be observed. Firstly, income inequality has increased onaverage across the sample for each country. The absolute levels in the United States and Canada aregreater than those observed in the United Kingdom4. Furthermore, there is no indication that incomeinequality in the United States is likely to decrease in the future whereas the case for declininginequality can observationally be made for the United Kingdom and potentially for Canada. Themodels for the United States and Canada indicate that the value of the Gini coefficient in 2013 (lastavailable datapoint) is roughly similar to the Gini that would have been observed if the trend of the pre-unconventional monetary policy were to have continued i.e. it qualitatively illustrates that quantitativeeasing (e.g.) had no effect on inequality. On the other hand, the model for the United Kingdom leads tothe conclusion that inequality is actually lower in 2013 than would have been expected if monetarypolicy had continued in the same fashion as before 2008 and the implementation of measures ofunconventional monetary policy. It is important to note that these are merely observational findingsthat abstract from other important factors and therefore this will need to be substantiated based onformal econometric analysis controlling forother confounders that may influence inequality.4 It is important to note that the measure of the Gini coefficient utilized are different between the countries due to dataavailability. The measure of the United States is a household aggregate (pre-tax), the United Kingdom is based ondisposable income, and Canada’s Gini is based on a market adjusted measure of income inequality.These measures willneed to be reconciled to more rigorously compare inequality across countries rather than simply within country across time. 2018 APRIL|InFER 83

RESEARCHB. Trends: Figure 6a: Trends of Gini Coefficients for the US .48 .47 .46 .45 .44 .43 .42 .41 .40 .39 1980 1985 1990 1995 2000 2005 2010 US GINI_TRE ND01 US GINI_TRE ND02 Gini_US The trend for the Gini coefficient for the United States has flattened out over the second half ofthe sample suggesting that inequality is not growing as quickly as it did over the first half of the sample. Figure 6b: Trends of Gini Coefficients for Canada.45.44.43.42.41.40.39.38.37.36 1980 1985 1990 1995 2000 2005 2010 GINITREND02 GINITREND01 Can_Gini84 InFER|2018 APRIL

Monetary Policy and its Effect on Inequality: The Role of Unconventional Monetary Policy Similarly to the time trajectory of the Gini coefficient for the United States, the mid-sample trend-split suggests that inequality in Canada has been decreasing on average since 1995. From 1977 through1995, inequality in Canada grew from approximately 0.365 to 0.44 Gini points. The trend-decline ofthe second half of the sample is much slighter, however illustrates a strong change from the earliertrendobserved. Figure 6c: Trends of Gini Coefficients for the UK The data for the Gini coefficient is available from 1977 to 2011. In order to estimate the trend forthe Gini, the data has been split in half and two trends generates. 38 36 34 32 30 28 26 24 5 10 15 20 25 30 35 Gini GINITREND01 GINITREND02 Ultimately, the above three graphs illustrate that for the countries of this sample, the UnitedStates is the only that has experienced an increase in income inequality (as represented by the Ginicoefficient) since approximately the mid-1990s as illustrated by the trends. Furthermore,observationally, if quantitative easing indeed increased income inequality in the countries that utilizedit as a monetary policy tool, we would expect some indication of a uniform increase in the trendsassociated with the UK and the US over the latter-half of the sample due to the recent period’s increase.While this may be observed for the United States, it is not so for the United Kingdom. This suggeststhat perhaps there are other forces driving this divergence between the evolutions of income inequalityin two QE countries. 2018 APRIL|InFER 85

RESEARCHC. Initial bivariate empirical model:gt = α0 + β1 gt-1 + β2MBt-1 + β3MBt-2 (1) Canada log Gini (2) (3) Intercept -0.197* (0.099) UK log Gini US log Gini Log Gini_1 0.836*** (0.078) -0.133 (0.089) -0.028 (0.031) Money Base_1 0.149 (0.099) 0.869*** (0.075) 0.977*** (0.038) Money Base_2 -0.061 (0.111) 0.131 (0.100) -0.056 (0.107) R-squared 0.93 -0.156 (0.107) 0.084 (0.120) Durbin-Watson 1.7 0.86 0.97 2.7 1.97 Sample 1979-2013 1979-2011 1979-2013D. The time series-based, autoregressive distributive lag leads to the following empirical results. Variables (1) (2) (3) Canada log Gini UK log Gini US log Gini Intercept -0.635 (0.577) -0.179 (0.226) -0.543* (0.277) Log Gini_1 0.608** (0.238) 0.841*** (0.130) 0.659*** (0.178) Money Base_1 0.252** (0.121) 0.188 (0.125) -0.019 (0.147) Money Base_2 -0.048 (0.129) -0.218 * (0.125) 0.193 (0.142) Log TLP 0.255 (0.351) 0.630 (0.381) 0.082 (0.155) Log TLP_1 -0.228 (0.335) -0.614 (0.410) -0.019 (0.147) Real LTRT 0.006* (0.003) -0.003 (0.003) -0.00006 (0.002) Real LTRT_1 -0.002 (0.003) 0.002 (0.003) 0.001 (0.001) Trade (/GDP) -0.002 (0.001) -0.0007 (0.004) -0.101 (0.177) Trade (/GDP)_1 0.003** (0.001) -0.00007 (0.003) 0.112 (0.191) R-sq 0.95 0.88 0.97 Durbin-Watson 1.96 2.7 1.65 Sample 1979-2011 1979-2011 1979-2013E. Theory-Based model: Variable Canada Log Gini UK Log Gini US Log Gini Intercept -2.529 (0.407) -0.226 (0.241) -0.509** (0.222) Log Gini_1 -0.097 (0.167) 0.74*** (0.162) 0.527*** (0.169) Log Labor Prod. 0.307 (0.059) 0.062 (0.083) 0.046 (0.029) Money Base _1 0.01 (0.048) -0.014 (0.766) -0.076 (0.053) Unemployment 0.958 (0.244) -0.147 (0.776) 0.327** (0.14)86 InFER|2018 APRIL

Monetary Policy and its Effect on Inequality: The Role of Unconventional Monetary PolicyGov’t Expenditure (/ GDP) 1.107 (0.27) -0.856 (1.045) -1.14** (0.476)Trade (/GDP) 0.003 (0.0005) 0.0003 (0.917) 0.036 (0.106)R- Squared 0.94 0.84 0.98Durbin Watson 1.7 2.4 1.8Sample 1980-2011 1980-2011 1978-2013 From the tables above, it can be noted that monetary policy is inconsistently significant acrossmodels and countries suggesting that (for the overwhelming majority of cases, insignificantly associatedwith income inequality), based on this research for these countries and sample, there is no robustevidence that monetary policy has a strong association with income inequality – either exacerbating orreducing inequality. This is striking because the findings suggest that for these countries and time-sample, income inequality as explained by both time-series characteristics and theory-based suggestionsis not significantly associated with monetary policy as proxied through the money base. The finalincluded model will be utilized in order to confirm the consistency of our findings across models or tochallenge them with a more complex model. Specifically, Saiki and Frost (2014) find significanceutilizing a VAR and controlling for the portfolio channel by stock prices, so can the same be found forthe US, UK and Canada?F. Vector Autoregression, Orthagonalized Impulse Responses of Gini Coefficient to the Money Base:Response to Cholesky One S.D. Innovations ± 2 S.E. Response to Cholesky One S.D. Innovations ± 2 S.E. Response of CGINI to LCMBSHGDP(-1) Response of UKGINI to LUKMBSHGDP(-1) .008 .010 .004 .005 .000 .000-.004-.008 -.005 2 4 6 8 10 2 4 6 8 10 Response to Cholesky One S.D. Innovations ± 2 S.E. Response of USGINI to LUSMBSH(-1) .006 .004 .002 .000 -.002 2 4 6 8 10 2018 APRIL|InFER 87

RESEARCH The results from the impulse response functions as it pertains to the response of the Gini coefficient to a shock to the Money Base is consistent with the aforementioned findings from the previous models. It can be observed that there is no significant response of the Gini coefficient to the money base particularly so for the case of the United Kingdom and the United States – the two countries in our sample that implemented Quantitative Easing. The resultant graph for Canada is perhaps less clear, however, at best the association is weakly significant, particularly so past the third period. Overall, this provides a similar result to the aforementioned findings based on a more complex model that is in line with the underlying conclusion that there is no strong evidence in support of the claim that monetary policy is significantly associated with income inequality for the countries of our sample – two of which implemented Quantitative Easing following the Financial Crisis (the UK and the US) and one of which did not (Canada).5. Conclusion There has been much discussion revolving around the association between income inequality and monetary policy, particularly so following the financial crisis and the bail-outs of banks and potential shifts in monetary policy that favor the re-concentration of wealth in the hands of the wealthiest individuals in a country. Our research suggests that there is no strong evidence that there exists a significant association between monetary policy and income inequality for Canada, the United Kingdom nor the United States according to findings based on three models that account for time series characteristics, suggestions provided by theory and published literature, as well as a more complex multi- equation model (VAR), respectively. While there is some comfort in the consistency of our findings, future prospects of similar research could utilize household-level data to provide a synthesized view of both the micro- and macro-elements of inequality in a country. In addition, continued research could utilize other proxies of monetary policy for a more complete understanding of the dynamics between monetary policy and income inequality.6. Sources Cited Acemoglu, D., & Johnson, S. Who Captured the Fed? The New York Times, 2012. Available by: http://economix.blogs.nytimes.com/2012/03/29/who-captured-the-fed/?_r=0. Alvaredo, F., et al. The top 1 percent in international and historical perspective. No. w19075.National Bureau of Economic Research, 2013. Atkinson, A. B., Piketty, T. & Saez, E. Top incomes in the long run of history. No. w15408. National Bureau of Economic Research, 2009. Birchenall, J.A. Income distribution, human capital and economic growth in Colombia. Journalof Development Economics, 2001. Bivens, J. Raising America’s Pay. Economic Policy Institute, 2014. Available by: http://www.epi.org/publication/raising-americas-pay/88 InFER|2018 APRIL

Monetary Policy and its Effect on Inequality: The Role of Unconventional Monetary PolicyChapman, G. S. The Problem of Income Inequality in South Africa. 2012Chowdhury, M. J. A. Does Access to Finance Reduce Inequality? Evidence from Bangladesh. University of Dhaka, 2010.Coibion, A., Gorodnichenko, Y., Kueng, L., & Silva, J. Innocent Bystanders? Monetary Policy and Inequality in the U.S. SSRN Electronic Journal, 2012.Deininger, K., Squire, L. New ways of looking at old issues: Inequality and growth. Journal of Development Economics, 1998.Demirgüç-Kunt, A., & Levine, R. Finance and Inequality: Theory and Evidence. Annual Review of Financial Economics, 2009.Facundo, A., Atkinson, A. B., Piketty, T., & Saez, E. The Top 1 Percent in International and Historical Perspective. Journal of Economic Perspectives, 2013.Fischer, R. D. The evolution of inequality after trade liberalization. Journal of Development Economics, 2001.Fischer, R. D., Huerta, D., & Valenzuela, P. Inequality and Private Credit. 2010.Owyang, M. T., & Shell, H. G. Taking Stock: Income Inequality and the Stock Market. 2016.Piketty, T., & Saez, E. Income Inequality in the United States, 1913-1998 (series updated to2000 available). No. w8467. National bureau of economic research, 2001.Piketty, T., & Saez, E. The evolution of top incomes: a historical and international perspective. No. w11955. National Bureau of Economic Research, 2006.Romer, C. D., & Romer, D. H. Monetary policy and the wellbeing of the poor. Federal Reserve Bank of Kansas City, Proceedings, 1998.Saiki, A., & Frost, J. How does Unconventional Monetary Policy Affect Inequality? Evidence fromJapan. DNB Working Paper No. 423, 2014.Spilimbergo, A., Londoño, J. L., & Székely, M. Income distribution, factor endowments, and trade openness. Journal of Development Economics, 1999.Warsh, K. Kevin Warsh: Fed Policy is “Reverse Robin Hood”. The MarketWatch, 2014. Availableby: http://www.marketwatch.com/story/kevin-warsh-fed-policy-is-reverse-robin-hood-2014-06- 26 2018 APRIL|InFER 89

RESEARCHAppendix:A: Impulse Response for Canada ResponsetoCholeskyOneS.D. Innovations ±2S.E. Response of LUSGDP to LUSGDP Response of LUSGDP toUSINFL Response of LUSGDP to LUSMBSH(-1) Response of LUSGDP to LUSDJAVG(-1) Response of LUSGDP to USGINI .06 .06 .06 .06 .06 .04 .04 .02 .04 .04 .04 .02 .00 .00 -.02 .02 .02 .02 -.02 -.04 -.04 .00 .00 .00 2 4 6 8 10 2 4 6 8 10 -.02 -.02 -.02 Response of USINFL to LUSGDP Response of USINFL to USGINI 2 -.04 -.04 -.04 2 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 Response of USINFL to USINFL Response of USINFL to LUSMBSH(-1) Response of USINFL to LUSDJAVG(-1) 2 2 2 11111 0 00 0 0 -1 -1 -1 -1 -1 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 Response of LUSMBSH(-1) to LUSGDP Response of LUSMBSH(-1) to USINFL Response of LUSMBSH(-1) toLUSMBSH(-1) Response of LUSMBSH(-1) to LUSDJAVG(-1) Response of LUSMBSH(-1) to USGINI .08 .08 .08 .08 .08 .04 .04 .04 .04 .04 .00 .00 .00 .00 .00 -.04 -.04 -.04 -.04 -.04 -.08 -.08 -.08 -.08 -.08 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 Response of LUSDJAVG(-1) to LUSGDP Response of LUSDJAVG(-1) to USINFL Response of LUSDJAVG(-1) to LUSMBSH(-1) Response of LUSDJAVG(-1) toLUSDJAVG(-1) Response of LUSDJAVG(-1) to USGINI .15 .15 .15 .15 .15 .10 .10 .10 .10 .10 .05 .05 .05 .05 .05 .0 0 .0 0 .0 0 .0 0 .0 0 - .0 5 - .0 5 - .0 5 - .0 5 - .0 5 - .1 0 - .1 0 - .1 0 - .1 0 - .1 0 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 .006 Response of USGINI to LUSGDP .006 Response of USGINI to USINFL Response of USGINI to LUSMBSH(-1) Response of USGINI to LUSDJAVG(-1) .006 Response of USGINI to USGINI .004 2 4 6 8 10 .004 2 4 6 8 10 .006 .006 .004 2 4 6 8 10 .002 .002 .002 .000 .000 .004 .004 .000 -.0 02 -.0 02 -.0 02 .002 .002 .000 .000 -.0 02 -.0 02 2 4 6 8 10 2 4 6 8 10B: Impulse Response for the United Kingdom Response to CholeskyOne S.D. Innovations ± 2 S.E. Response of LCGDP to LCGDP Response of LCGDP to CINFL Response of LCGDP to LCMBSHGDP(-1) Response of LCGDP to LCSTOCK(-1) Response of LCGDP to CGINI .0 4 .0 4 .0 4 .0 4 .0 4 .0 3 .0 3 .0 3 .0 3 .0 3 .0 2 .0 2 .0 2 .0 2 .0 2 .0 1 .0 1 .0 1 .0 1 .0 1 .0 0 .0 0 .0 0 .0 0 .0 0 -.01 -.01 -.01 -.01 -.01 -.02 -.02 -.02 -.02 -.02 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 Response of CINFL toLCGDP Response of CINFL to CINFL Response of CINFL to LCMBSHGDP(-1) Response of CINFL to LCSTOCK(-1) Response of CINFL to CGINI 1.5 1.5 1.5 1.5 1.5 1.0 1.0 1.0 1.0 0.5 1.0 0.0 0.5 0.5 0.5 0.5 -0.5 2 4 6 8 10 0.0 0.0 0.0 0.0 -0.5 -0.5 -0.5 -0.5 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 Response of LCMBSHGDP(-1) to LCGDP Response of LCMBSHGDP(-1) to CINFL Response of LCMBSHGDP(-1) to LCMBSHGDP(-1) Response of LCMBSHGDP(-1) to LCSTOCK(-1) Response of LCMBSHGDP(-1) to CGINI .0 8 .0 8 .0 8 .0 8 .0 8 .0 4 .0 4 .0 4 .0 4 .0 4 .0 0 .0 0 .0 0 .0 0 .0 0 -.04 -.04 -.04 -.04 -.04 -.08 -.08 -.08 -.08 -.08 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 Response of LCSTOCK(-1) to LCGDP Response of LCSTOCK(-1) to CINFL Response of LCSTOCK(-1) to LCMBSHGDP(-1) Response of LCSTOCK(-1) to LCSTOCK(-1) Response of LCSTOCK(-1) to CGINI .4 .4 .4 .4 .4 .3 .3 .3 .3 .3 .2 .2 .2 .2 .2 .1 .1 .1 .1 .1 .0 .0 .0 .0 .0 - .1 - .1 - .1 - .1 - .1 - .2 - .2 - .2 - .2 - .2 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 .0 08 Response of CGINI to LCGDP .0 08 Response of CGINI to CINFL Response of CGINI to LCMBSHGDP(-1) Response of CGINI to LCSTOCK(-1) .0 08 Response of CGINI to CGINI .0 04 2 4 6 8 10 .0 04 2 4 6 8 10 .0 08 .0 08 .0 04 2 4 6 8 10 .0 00 .0 00 .0 00 -.0 04 -.0 04 .0 04 .0 04 -.0 04 -.0 08 -.0 08 -.0 08 .0 00 .0 00 -.0 04 -.0 04 -.0 08 -.0 08 2 4 6 8 10 2 4 6 8 1090 InFER|2018 APRIL

Monetary Policy and its Effect on Inequality: The Role of Unconventional Monetary PolicyC: Impulse Response for the United States Response to CholeskyOne S.D. Innovations ± 2 S.E. Response ofLUK GDPto LUKGDP Response ofLUKGDPto UKINFL Response ofLUKGDPto LUKMBSHGDP(-1) Response ofLUKGDPto LUKSTOCK(-1) Response of LUKGDPto UKGINI .04 .04 .04 .04 .04 .02 .02 .00 .02 .02 .02 .00 -.02 -.02 -.04 .00 .00 .00 -.04 2 4 6 8 10 -.02 -.02 -.02 2 4 6 8 10 Response ofUKINFLtoLUKGDP -.04 -.04 -.04 Response of UKINFL to UKGINI 2 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 1 Response of UKINFL to UKINFL Response ofUKINFL to LUKMBSHGDP(-1) Response ofUKINFL to LUKSTOCK(-1) 1 2 2 2 0 0 111 -1 -1 2 4 6 8 10 000 2 4 6 8 10 Response ofLUKMBSHGDP(-1) toLUKGDP -1 -1 -1 Response of LUKMBSHGDP(-1) to UKGINI .2 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 .2 .1 .1 .0 Response ofLUKMBSHGDP(-1) toUKINFL Response ofLUKMBSHGDP(-1) toLUKMBSHGDP(-1) Response ofLUKMBSHGDP(-1) toLUKSTOCK(-1) .0 -.1 .2 .2 .2 -.1 -.2 -.2 .1 .1 .1 2 4 6 8 10 2 4 6 8 10 .0 .0 .0 Response ofLUKSTOCK(-1) toLUKGDP Response of LUKSTOCK(-1) to UKGINI .2 -.1 -.1 -.1 .2 .1 .1 .0 -.2 -.2 -.2 .0 -.1 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 -.1 -.2 -.2 Response ofLUKSTOCK(-1) to UKINFL Response ofLUKSTOCK(-1) to LUKMBSHGDP(-1) Response ofLUKSTOCK(-1) to LUKSTOCK(-1) 2 4 6 8 10 .2 .2 .2 2 4 6 8 10 Response ofUKGINItoLUKGDP .1 .1 .1 Response of UKGINIto UKGINI.010 .010 .0 .0 .0.005 .005 -.1 -.1 -.1.000 -.2 -.2 .000 -.2-.005 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 -.005 2 4 6 8 10 2 4 6 8 10 Response of UKGINIto UKINFL Response of UKGINIto LUKMBSHGDP(-1) Response of UKGINIto LUKSTOCK(-1) .010 .010 .010 .005 .005 .005 .000 .000 .000 -.005 -.005 -.005 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2018 APRIL|InFER 91

InFERInternational Finance and Economics Review library(\"insights\") infer <- function(x) { x <- read.data (world) plot (x=time, y=reality) analyze (x) x }

April 2018 Trial IssueArticleThe United States of NorthAmerica: Should Canada andMexico Dollarize?ResearchThe Role of Theory-MotivatedFundamentals in Long-RunExchange Rate ForecastingMonetary Policy and its Effecton Inequality: The Role ofUnconventional Monetary Policy