Capital accumulation for credit constrained firms in Kiyotaki and Moore (1997)
This appendix derives a dynamic capital accumulation equation for credit constrained firms, using equilibrium conditions for ‘farmers’ as in Kiyotaki and Moore (1997). For ease of comparison, we use KM’s notation and then map equations to our own notation at the end.
The variables are: k=capital; q=capital price; b=borrowing; R=real interest rate; a=traded output. Equilibrium values are denoted by *.
The borrowing constraint is characterized (page 218 eq 3) by:
The equilibrium is characterized (page 220, around eq 7) by:
where the denominator
Then divide and multiply the rightmost expression by
In the body of the text, we use capital K=ln(k) and the credit limit CL=ln(cl) in logarithmic form. Equation (A3) then becomes:
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The paper was written when Rima Turk Ariss was Associate Professor at the Lebanese American University and was later revised after joining the IMF-Middle East Center for Economics and Finance.
The authors thank Chadi Abdallah, Hein Boggard, Philippe Karam, May Khamis, Dmitriy Rozhkov, Fabio Verona, and Bruno Versailles, for helpful comments and suggestions as well as participants at the BOFIT seminar, the Finnish Economic Society, and the Financial Management Association meeting.
See Bhaumik, Das, and Kumbakhar (2012) and Abdallah and Latrapes 2012() for alternative approaches. Bhaumik, Das, and Kubakhar 2012() quantify the impact of borrowing constraints on capital accumulation by comparing the prevailing investment to capital ratios to their optimal level, which they estimate using the stochastic frontier method. Abdallah and Latrapes 2012() make use of an exogenous change in the law as a natural experiment to estimate the importance of credit constraints for households.
Recent evidence by Bloom 2009() indicates that shocks related to the onset of political instability have significant but temporary negative effects on corporate investment and economic growth.
Arab Spring countries include Egypt, Syria, and Tunisia. Both Egypt and Tunisia are a subset of Arab Countries in Transition that include Egypt, Jordan, Libya, Morocco, Tunisia, and Yemen.
By construction, DL is unobservable, akin to CL.
We do not use panel estimators to avoid imposing undue restrictions on residual parameters in time.
Based on data availability, the countries covered are: Bahrain, Egypt, Iraq, Jordan, Kuwait, Lebanon, Morocco, Oman, Qatar, Saudi Arabia, Sudan, Syrian Arab Republic, Tunisia, and United Arab Emirates, and West Bank and Gaza.
Our baseline regressions do not include countries with a very low number of firms with available data (i.e., Lebanon, Sudan, and Syria). However, robustness checks indicate that including them does not affect our results.
We distinguish between Arab Spring countries and countries that experience political unrest for two reasons. First, Arab Spring countries did not experience political unrest during our sample period and the uprising came about in 2011. Second, political unrest in the other countries has been on-going for an extended period of time.
This interpretation is not at variance with Table 6, since the estimates of DL for individual firms are expected values.
The tabulations of the robustness checks are available upon request from the authors.