How Inclusive Is Abenomics?; by Chie Aoyagi, Giovanni Ganelli, and Kentaro Murayama; imf working Paper No. 15/54; March 1, 2015

 28 

and solving for x, we can show that the maximum effect reached at the inflation level of 

1.586/0.706 = 2.246 %; and the maximum value would be 1.781%. 

 

 

The marginal effect of inflation depends on the initial value: 

 

 

1.586

–  0.353

1.586

–  0.353

 

In the text chart, we plot the marginal effect of changes in inflation rates (red line), while 

assuming an initial inflation rate of 0.00% as in our policy scenario. The chart shows an 

initially increasing, but then 

diminishing marginal effect. 

Moreover, the marginal effect 

becomes negative (i..e further 

inflation reduces inclusive growth) 

at around 4.5%. Note that, because 

the specified curve is symmetric, the 

marginal effect would decay off at 

the same distance from the optimal 

level. In this case, it is 

2.246

 2.246

0    4.492%. 

 

The policy scenario we considered is 

the initial value of 0.00% and the 

targe rate of 2.00% (text chart, green 

line). With an increase of 2.00% 

points, the marginal effect on the 

inclusive growth is 1.76%, slighlty 

less than the value at the optimal level. 

 

 

 

---

 29 

Appendix D. Causality Direction between Inflation and Growth  

 

To test endogeneity, we run simple bilateral regressions between growth and inflation: 

y

a y

‐

a y

‐

b m

‐

b m

‐

μ v  

 

where   is the dependent variable and   is the (supposedly endogenous) explanatory 

variables. Note that this is not equivalent to a conventional Grange causilitu test because: the 

lag is not chosen by statistical significance, but limited by the data availability (l=2);  

regressions are run separately; and the specification contains the fixed effect for each 

prefecture.  

 

The result is shown in the table below.  

Dependent variable: 

Growth 

Inflation 

(1) 

(2) 

lag(dys, 1) 

-0.461

***

 

0.080

**

 

(0.110) 

(0.039) 

lag(dys, 2) 

-0.078 

0.094

**

 

(0.104) 

(0.037) 

lag(Inflation, 1) 

2.052

***

 

0.962

***

 

(0.251) 

(0.090) 

lag(Inflation, 2) 

1.431

***

 

0.816

***

 

(0.093) 

(0.033) 

Observations 

144 

144 

R

2

 

0.748 

0.918 

Adjusted R

2

 

0.478 

0.587 

F Statistic (df = 4; 92) 68.230

***

 

258.300

***

 

Note: 

*

p<0.1; 

**

p<0.05; 

***

p<0.01 

 

Both variables are good leading indicator of the other both at the lag of 1 and 2, but the 

coefficients on the impact of inflation on growth tend to be larger than those of the impact on 

griwth on inflation.  

 

 

---

 30 

We have also estimated the same model as in the becnhamrk case, btu with with lagged (l=1) 

inflation (5 year averages) as an instrument variable (Balestra & Varadharajan-

Krishnakumar, 1987). The results are shown below, and are broadly consistens with those 

discussed in the main text. 

 

Table 1 

Results for All Income, IV 

Dependent variable: 

dys 

dy 

dw 

(1) 

(2) 

(3) 

Inflation (%) 

4.707

***

4.592

***

0.051 

(1.154)  (1.071)  (0.259)

Inflation, squared 

-0.876

***

-0.832

***

-0.034 

(0.195)  (0.181)  (0.044)

Part- to Full-time job opennings (%) 0.031 

0.023 

0.007 

(0.038)  (0.035)  (0.009)

Female labor force participation (%) 0.270

*

  0.225

*

  0.042 

(0.137)  (0.127)  (0.031)

Labor input growth (%) 

0.156 

0.136 

0.019 

(0.291)  (0.270)  (0.065)

Initial GDP per capita 

-5.476

***

-4.737

***

-0.707

*

(1.812)  (1.683)  (0.407)

Elderly index 

0.450

***

0.429

***

0.014 

(0.153)  (0.142)  (0.034)

Observations 

235 

235 

235 

R

2

 

0.486 

0.539 

0.105 

Adjusted R

2

 

0.374 

0.415 

0.081 

F Statistic (df = 7; 181) 

5.173

***

7.330

***

3.021

***

Not

e: 

*

p<0.1; 

**

p<0.05; 

***

p<0.01 

---

 31 

Results for Working-age Income, IV

Dependent variable: 

dys.work dy.work dw.work

(1) 

(2) 

(3) 

Inflation (%) 

4.926

***

  4.371

***

0.534 

(1.226)  (1.047)  (0.324) 

Inflation, squared 

-0.852

***

-0.743

***

-0.106

*

 

(0.207)  (0.177)  (0.055) 

Part- to Full-time job opennings (%) 0.025 

0.014 

0.011 

(0.040)  (0.034)  (0.011) 

Female labor force participation (%) 0.338

**

  0.250

**

  0.088

**

 

(0.146)  (0.124)  (0.038) 

Labor input growth (%) 

-0.020 

0.018 

-0.039 

(0.309)  (0.264)  (0.082) 

Initial GDP per capita 

-4.770

**

  -3.545

**

-1.230

**

(1.926)  (1.645)  (0.509) 

Elderly index 

0.497

***

  0.417

***

0.079

*

 

(0.162)  (0.139)  (0.043) 

Observations 

235 

235 

235 

R

2

 

0.444 

0.514 

0.007 

Adjusted R

2

 

0.342 

0.396 

0.005 

F Statistic (df = 7; 181) 

-0.283 

5.466

***

-4.416 

Note: 

*

p<0.1; 

**

p<0.05; 

***

p<0.01

 

 

 

 

---

 32 

Appendix E. Contributions of regressors to variation in equity.  

 

In the text table below me represent various measures of how much of the variation in the 

equity index is explained by the various regressors. The top three variables for each measure 

are denoted by ***. 

 

Standardized Regression Coefficients show the expected change of the dependent variable in 

standard deviations with respect to one standard deviation change in the explanatory variable. 

(e.g. one standard deviation change in FLP is associated with a 0.373 standard deviation 

change in equity index growth).  

Semi-Partial Correlation Coefficients measure the unique contribution of each explanatory 

variable in explaining the variations of the dependent variable. The proportion of the 

variation that is jointly explained by multiple variables is not accounted for in this measure 

(i.e. if all the explanatory variables are independent of each other, the set of semi-partial 

correlation coefficients sum up to the R^2 of the model.) 

Extra Sum of Squares is simply the amount of sum of squared residuals reduced by removing 

one variable from the full model. (e.g. by removing inflation the sum of squared residuals is 

increased by 0.707, by removing inflations squared it is increase by 0.321). Note that they do 

not sum up to the total sum of squared residuals. 

 

Contributions of regressors to variation in equity. 

  

Standardized 

Regression 

Coefficients 

Semi-Partial 

Correlation 

Coefficients 

Extra Sum 

of Squares 

Inflation 

-0.089 0.005*** 

0.707*** 

Inflation, squared 

-0.056 0.006*** 

0.321*** 

Job Openings 

0.132*** 0.001  0.089 

FLP 

0.373*** 0.007***  0.254 

Labor Growth 

0.069 0.0005 

0.032 

GDP PC 

-0.58*** 0.004 

0.757*** 

Elderly Index 

0.079 0.0001 

0.017 

  

- 0.0236 

- 

 

 

 

 

 

 

 

 

 

---

 33 

 

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