Finance and Economics Discussion Series: Accessible versions of figures for 2015-063

Aggregate Consequences of Dynamic Credit Relationships

Accessible version of figures


Figure 1: Timing within a period. Figure 1 is a timeline that describes the timing within a period.

Decision node 1: begins the timeline. The upper branch refers to "continue" and the bottom branch refers to "liquidate." Decision node 2 and 3 branches out from the Decision node 1. The upper branch of Decision node 3 refers to the "monitoring" and the lower branch refers to "no monitoring." The upper branch of Decision node 2 refers to "to entrepreneur" and the lower branch refers to "to intermediary." Period 2 stops branching out at this point.

Decision node 3 branches out to two main branches (an upper (4a) and a lower branch (4b)). Each of these branches are divided into five or six different Decision nodes.

The upper branch (4a) lists the following six Decision nodes: 4a1 refers to Intermediary advances. 4a2 refers to Nature draws. 4a3 refers to Entrepreneur reports. 4a4 refers to Entrepreneur transfers. 4a5 refers to Audit. 4a6 refers to Exit with probability gamma The branch ends with period $$h_t = \{h_{t-1}, v\}$$.

The lower branch (4b) lists the following five Decision nodes: 4b1 refers to Intermediary advances. 4b2 refers to Defaults. 4b3 refers to Entrepreneur diverts and search for new project. 4b4 refers to Entrepreneur transfers. 4b5 refers to Exit with probability gamma The branch ends with period $$h_t = \{h_{t-1}, \tilde{v}\}$$.

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Figure 2: Optimal loan size $$ R(V)$$ and continuation values $$ V^{\prime}(V)$$

Figure 2 contains four separate line charts. The (a) charts refer to the top and bottom charts on the left hand side. The (b) charts refer to the top and bottom charts on the right hand side. Figure 2 (a) charts depicts the decision rules with no monitoring under both the weak and strong enforcement. Figure 2 (b) charts depict the decision rules with full monitoring under weak and strong enforcement.

Figure 2 (a) upper left hand graph is a line chart that depicts the decision rules for loan size R(V) with no monitoring. The x-axis is V and it ranges from 0 to$$\tilde{V}$$. The y-axis is R(V) and it ranges from 0 to $$\tilde{R}$$. There are two lines depicted in this graph. The solid red line is loan size value under strong enforcement. The blue dashed line is loan size value under weak enforcement. The solid red line starts at a low value of V and increases at a decreasing rate until it reaches $$\tilde{R}$$ when V is equal to $$\tilde{V}$$. The blue dashed line starts at low but higher value of V and increases at a decreasing rate until it reaches $$\tilde{R}$$ when V is equal to $$\tilde{V}$$.The blue dashed line is always under the solid red line.

Figure 2 (b) upper right hand graph is a line chart that depicts the decision rules for loan size R(V) with full monitoring. The x-axis is V and it ranges from 0 to $$\tilde{V}$$. The y-axis is R(V) and it ranges from 0 to $$\tilde{R}$$. There are two lines depicted in this graph. The solid red line is loan size value under strong enforcement. The blue dashed line is loan size value under weak enforcement. The solid red line starts at a low value of V and increases at a slightly increasing rate until it reaches $$\tilde{R}$$. This happens for value of V that are less than $$\tilde{V}$$. The blue dashed line starts at low value of V and increases at a slightly increasing rate until it reaches $$\tilde{R}$$. This happens for value V that are less than $$\tilde{V}$$ and the blue dashed line is always under or on the solid red line.

Figure 2(a) lower left hand graph is a line chart that depicts the promised continuation values with no monitoring. The x-axis is V and it ranges from 0 to $$\tilde{V}$$. The y-axis is the continuation value V'(V) and it ranges from 0 to $$\tilde{V}$$. There are four lines depicted in this graph. In addition, the black dashed line refers to the 45 degree line. The red solid line, above the 45 degree line, is the promised continuation value conditional on high revenue shock under strong enforcement. The blue dashed line, above the 45 degree line, is the promised continuation value conditional on high revenue shock under weak enforcement. The red solid line, below the 45 degree line, is the promised continuation value conditional on low revenue shock under strong enforcement. The blue dashed line, below the 45 degree line, is the promised continuation value conditional on low revenue shock under weak enforcement. The red solid and blue dashed lines, above the 45 degree line, follow a similar pattern. The lines starts at low value of V at which point V'(V) is also low. V'(V) conditional of low revenue shock increases at an increasing rate until it reaches $$\tilde{V}$$ when V is equal to $$\tilde{V}$$. The red solid and blue dashed lines, below the 45 degree line, follow a similar pattern. The lines starts at low value of V at which point V'(V) is also low. V'(V) conditional of high revenue shock increases at an decreasing rate until it reaches $$\tilde{V}$$ when V is equal to $$\tilde{V}$$. The difference between the lower and upper blue dashed line for a given V is always smaller than or equal to the difference between the lower and upper red solid line given the same V.

Figure 2(b) lower right hand graph is a line chart that depicts the promised continuation values with full monitoring. The x-axis is V and it ranges from 0 to $$\tilde{V}$$. The y-axis is the continuation value V'(V) and it ranges from 0 to $$\tilde{V}$$. There are four lines depicted in this graph. In addition, the black dashed line refers to the 45 degree line. The red solid line, above the 45 degree line, is the promised continuation value conditional on high revenue shock under strong enforcement. The blue dashed line, above the 45 degree line, is the promised continuation value conditional on high revenue shock under weak enforcement. The red solid line, on the 45 degree line, is the promised continuation value conditional on low revenue shock under strong enforcement. The blue dashed line, on the 45 degree line, is the promised continuation value conditional on low revenue shock under weak enforcement. The red solid and blue dashed lines, above the 45 degree line, follow a similar pattern. The lines starts at low value of V at which point V'(V) is also low. V'(V) conditional of low revenue shock increases linearly until it reaches $$\tilde{V}$$ when V is equal to $$\tilde{V}$$. The red solid and blue dashed lines, below the 45 degree line, follow a similar pattern. The lines starts at low value of V at which point V'(V) is also low. V'(V) conditional of high revenue shock increases linearly until it reaches $$\tilde{V}$$ when V is equal to $$\tilde{V}$$. The difference between the blue dashed line and the red solid line is that the blue dashed line start at a higher V value.

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Figure 3: Firm dynamics

Figure 3 has two line charts. The top line chart is investment growth rate conditional on firm age. The bottom chart is the volatility of investment growth rate conditional on firm age.

The top chart is a line chart that depicts the investment growth rate conditional on firm age in years. The x-axis is the firm age and it ranges from 0 to 60 years. The y-axis is the percent of investment growth rate which ranges from 0 to 25. There are four trends that are depicted in individual lines. The solid blue line is the full monitoring and weak enforcement. The dashed blue line is the full monitoring and strong enforcement. The solid red line is the no monitoring and weak enforcement. The dashed red line is no monitoring and strong enforcement. The dashed blue line starts at firm age 1 at it is at 12 percent. It makes a downward trend to 0 percent at firm age 9. It continues to stay at 0 percent for the remaining firm age. The solid blue line starts at firm age 1 at 25 percent. It makes a downward slope till it hits 0 percent at firm age 15. It continues to stay at 0 percent for the remaining firm age. The red dashed line start at firm age 1 and 9 percent. It makes a downward slope till it hits 1 percent at around firm age 50 and continues to hover around 1 percent for the remaining firm age periods. The solid red line starts at firm age 1 and 12 percent. It increases to 15 percent at firm age 5 and goes up to 20 at firm age 6. It continues to go up and down from 20 to 25 till firm age 10. Then it starts a downward trend with slight periodic increases till it hovers between 0 and 1 percent around firm age 50. This pattern continues till the end of the firm age.

The bottom chart is a line chart that depicts the volatility of investment growth rate conditional on firm age. The x-axis is the firm age and it ranges from 0 to 60 years. The y-axis is the standard deviation of growth rate which ranges from 0 to 70. There are four trends that are depicted in individual lines. The solid blue line is the full monitoring and weak enforcement. The dashed blue line is the full monitoring and strong enforcement. The solid red line is the no monitoring and weak enforcement. The dashed red line is no monitoring and strong enforcement. The blue dashed line starts at firm age 1 and standard deviation of 11. It makes a downward sloping trend till it reaches 0 standard deviation at period 15 and continues for the remaining firm age periods. The blue line starts at firm age 1 with a standard deviation of 25. It makes a downward sloping trend till it reaches 0 standard deviations at firm age 19. It continues and 0 for the remaining firm age. The red dashed line begins at firm age 1 and a standard deviation of 39. It makes a downward trend till it ends at firm age 60 and standard deviation of 11. The solid red line start at firm age 1 and a standard deviation of 51. It increases to 70 and firm age 5. Slight up and down patterns between 65 and 70 standard deviation till firm age 9. Then a downward trend till it ends at firm age 60 and 15 standard deviations.

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Figure 4: Firm size distribution

Figure 4 is a line chart that depicts the Average firm size conditional on firm age. The x-axis is the firm age and it ranges from 0 to 30 years. The y-axis is the average firm size normalized by the unconstrained firm size and it ranges from 0 to 1. There are four trends that are depicted in individual lines. The solid blue line is the full monitoring and weak enforcement. The dashed blue line is the full monitoring and strong enforcement. The solid red line is the no monitoring and weak enforcement. The dashed red line is no monitoring and strong enforcement. The solid red line starts at firm age 1 and 0.225 firm size. It makes an upward trend till it reaches 0.825 at firm age 30. The red dashed line starts at firm age 1 and firm size 0.3. It makes and upward trend till it reaches 0.79 at firm age 30. The solid blue line starts at firm age 1 and firm size 0.3. It makes and upward trend till it reaches 1.0 firm size at firm age 15 and remains at 1.0 for the remaining firm age periods. The blue dashed line starts at firm age 1 and firm size 0.7. It makes and upward trend till it reaches 1.0 firm size at firm age 10. It remains at 1.0 for the remaining firm age periods.

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Figure 5: The effect of financial development

Figure 5 is a line chart that depicts the aggregate output response to a permanent strengthening of contract enforcement conditional on the monitoring costs. The x-axis is the years since reform and it ranges from 0 to 40. The y-axis is the percent deviation from previous steady state and it ranges from 0 to 1.6. There are two line trends that are depicted in this chart. The red dashed line is no monitoring and the blue dashed line is the full monitoring. The red line starts at period 1 years since reform and 0 percent. It makes a straight upward line till 5 years since reform and 1.5 percent. It then starts a downward trend till it reaches 40 years since reform and 0.3 percent. The blue dashed line starts at 1 year since reform and 0 percent. It makes a straight upward line till 4 years and 1.3 percent. Then it levels off at 1.3 percent for the remaining years since reform periods.

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Figure 6: The effect of technological shocks under weak enforcement

Figure 6 is a line chart that depicts the aggregate output response to a temporary improvement in blueprint technology with strong contract enforcement. The x-axis is the years since shock and it ranges from 1 to 15. The y-axis is the percent deviation from steady state and it ranges from -2.0 to +1.0. There are three trends depicted in this chart. The solid black line is for no friction. The red dashed line is for no monitoring. The dashed blue line is for full monitoring. All three lines have the same overlapping pattern. It starts at 1 year since shock and 0.39 percent. It decreases to 0.19 percent at 15 years since shock.

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Figure 7: The effect of technological shocks under strong enforcement

Figure 7 is a line chart that depicts the aggregate output response to a temporary improvement blueprint technology with weak contract enforcement. The x-axis is the years since shock and it ranges from 1 to 15. The y-axis is the percent deviation from steady state and it ranges from -2.0 to +1.0. There are three trends depicted in this chart. The solid black line is for no friction. The red dashed line is for no monitoring. The dashed blue line is for full monitoring. The solid black line starts at 1 year since shock and 0.39 percent. It ends at 15 years since shock and 0.19 percent. The blue dashed line starts at 1 year since shock and -1.8 percent. It makes a straight line increase till 2.5 years since shock and 0.6 percent. It makes a downward trend till 0.19 percent at 14 years since shock. The red dashed line starts at -0.9 percent at 1 years since shock. It makes a straight upward line till 0.7 at 2.5 years since shock. It starts to make a downward trend till it reaches 0.37 at 14 years since shock.

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