Presentation in 34th International Symposium on Forecasting, Rotterdam, June 29 - July 2, 2014

1. Stock-Flow Dynamic Projection
Stock-Flow Dynamic Projection
Mauro Gallegati Xihao Li
Department of Economics and Social Sciences (DiSES)
Universit `a Politecnica delle Marche
June 30, 2014
Mauro Gallegati, Xihao Li 34th International Symposium on Forecasting, Rotterdam

2. Stock-Flow Dynamic Projection Introduction Idea Example Concluding Remark
Introduction: I
Consider the Era of Big Data:
Economic Entities (firms/banks) provide accounting
statements for reporting: the balance sheet, the
income statement, the statement of cash flows;
in a faster pace, not only annual reporting but also
possibly quarterly or monthly reporting.
Mauro Gallegati, Xihao Li 34th International Symposium on Forecasting, Rotterdam

3. Stock-Flow Dynamic Projection Introduction Idea Example Concluding Remark
Introduction: II
Question: Can we take advantage of this new stream of
economic data?
to improve our capability of forecasting and
monitoring macroeconomic fluctuation, or even
crisis?
Mauro Gallegati, Xihao Li 34th International Symposium on Forecasting, Rotterdam

4. Stock-Flow Dynamic Projection Introduction Idea Example Concluding Remark
Idea: I
Experience from agent-based economic research:
economic agents’ micro-level interaction leads to
structural transition in meso-level which results in
macro-level economic fluctuation.
Two types of economic variables:
1 stock variable that measures quantities at a time
point, e.g. firms’ equity in the balance sheet;
2 flow variable that measures quantities at a time
interval, e.g. firms’ revenue in the income statement.
Mauro Gallegati, Xihao Li 34th International Symposium on Forecasting, Rotterdam

5. Stock-Flow Dynamic Projection Introduction Idea Example Concluding Remark
Idea: II
Main idea of Dynamic projection:
Macro-level economic variable = aggregation in
micro-level( stock / flow variable ) + aggregation in
meso-level( the impact of interaction among
economic entities ) (∗)
Assume ’as-if’ the economy in the future ceteris
paribus, compute dynamic projection for the future
state of macro-level economic variable by using
micro-level stock and flow data to measure each
component in formula (∗) .
Mauro Gallegati, Xihao Li 34th International Symposium on Forecasting, Rotterdam

6. Stock-Flow Dynamic Projection Introduction Idea Example Concluding Remark
Example
Use the dataset of Japanese firm’s financial statements 1:
for 4599 firms listed in Tokyo Stock Exchange
for 33 years of annual financial statements, i.e.
balance sheet, profit and loss statement(PL
statement)2, from the year of 1980 to 2012.
1
To use this dataset, the authors acknowledge the support from the European Community Seventh
Framework Programme (FP7/2007-2013) under Socio-economic Sciences and Humanities, grant
agreement no. 255987 (FOC-II)
2
Profit and loss statement is equivalent to income statement.
Mauro Gallegati, Xihao Li 34th International Symposium on Forecasting, Rotterdam

7. Stock-Flow Dynamic Projection Introduction Idea Example Concluding Remark
Example
Consider the following target variables:
stock variable: aggregate equity A from balance
sheet
flow variable: aggregate gross profit π from PL
statement.
Mauro Gallegati, Xihao Li 34th International Symposium on Forecasting, Rotterdam

8. Stock-Flow Dynamic Projection Introduction Idea Example Concluding Remark
Example
Dynamic projection for one-period-ahead out-of-sample
forecast, to compare with the benchmark of ARIMA:
1 Use data for period of 1980 to 1996 as initial
information set,
2 at the end of each period t = 1996, ..., 2011, compute
one-period-ahead out-of-sample forecast for X = A,
or π:
dynamic projection:
dp(X)t+1|t = {dp(X)1997|1996, . . . , dp(X)2012|2011}
choose the optimal ARIMA according to the
BIC(AICc) information criterion, then use the optimal
ARIMA to conduct the forecast:
ARIMA(X)t+1|t = {ARIMA(X)1997|1996, . . . , ARIMA(X)2012|2011}
Mauro Gallegati, Xihao Li 34th International Symposium on Forecasting, Rotterdam

9. Stock-Flow Dynamic Projection Introduction Idea Example Concluding Remark
Example
One-period-ahead out-of-sample forecast: aggregate equity
1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
120
140
160
180
200
220
240
260
year
aggregateequity
forecast: ARIMA Vs. dynamic projection
realization
ARIMA
dynamic projection
1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
−20
−10
0
10
20
year
aggregateequity
forecast error: ARIMA Vs. dynamic projection
ARIMA
dynamic projection
Mauro Gallegati, Xihao Li 34th International Symposium on Forecasting, Rotterdam

10. Stock-Flow Dynamic Projection Introduction Idea Example Concluding Remark
Example
One-period-ahead out-of-sample forecast: aggregate profit
1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
40
45
50
55
60
65
70
75
80
85
90
year
aggregategrossprofit
forecast: ARIMA Vs. dynamic projection
realization
ARIMA
dynamic projection
1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
−10
−5
0
5
10
year
aggregategrossprofit
forecast error: ARIMA Vs. dynamic projection
ARIMA
dynamic projection
Mauro Gallegati, Xihao Li 34th International Symposium on Forecasting, Rotterdam

11. Stock-Flow Dynamic Projection Introduction Idea Example Concluding Remark
Example
Diebold-Mariano test.
Null hypothesis: comparing with dp(X)t+1|t ,
ARIMA(X)t+1|t has the same or higher accuracy in
forecasting, for X = A, or π.
use linear loss function and quadratic loss function.
for aggregate equity A:
p-value Vs. ARIMA with BIC Vs. ARIMA with AICc
Power = 1 0.036 0.028
Power = 2 0.042 0.029
for aggregate gross profit π:
p-value Vs. ARIMA with BIC Vs. ARIMA with AICc
Power = 1 0.014 0.022
Power = 2 0.027 0.033
Mauro Gallegati, Xihao Li 34th International Symposium on Forecasting, Rotterdam

12. Stock-Flow Dynamic Projection Introduction Idea Example Concluding Remark
Concluding Remark
In our story of aggregate equity and aggregate
profit, dynamic projection shows higher accuracy in
one-period-ahead out-of-sample forecast than
ARIMA.
Is pure luck or any theory behind?
Working in progress: mathematical inference from
multi-level dynamical system. 3
3
See the MatheMACS project, supported under ”ICT-2011.9.7 FET Proactive: Dynamics of Multi-Level
Complex Systems (DyM-CS)”, http://www.mathemacs.eu/.
Mauro Gallegati, Xihao Li 34th International Symposium on Forecasting, Rotterdam

13. Stock-Flow Dynamic Projection Introduction Idea Example Concluding Remark
Thank you!
Mauro Gallegati, Xihao Li 34th International Symposium on Forecasting, Rotterdam