Transitional Dynamics Analysis

In this section, the speed of technology adoption and the speed of TFP convergence will be explored. The period studied is from 1986 to 2007. In 1986, the economy was in the state

17_{The values ofκ}U S

where only old technology was available. The Chilean economy started to have access to the technology ladder toward the world technological frontier in 1987. This is because, in 1987, Chilean manufacturing imports from high-income countries started to grow exponentially. Although the main reason import data are used as a proxy for foreign technology adoption is that the series are long enough to determine the transition period, the data on imports of machinery and equipment are also widely used in the literature as a proxy for foreign technology adoption [Caselli and Coleman II (2001); and Caselli and Wilson (2002)]. This is supported by the evidence that import activities are important channels for the transfer of technology [Almeida and Margarida Fernandes (2008)].

To simulate the transitional dynamics in response to the access to the technology ladder in 1987, two exogenous processes of real risk-free rates talents are given. These are treated as the expected processes. The fraction of new talented firms entering the economy is likely to increase over time when human capital and skills have been improving. This change is captured by changes in the parameters governing the conditional probability of being high type,κs,t, over time. Let κs,t =xtκs, whereκs represents the benchmark parameter values

calibrated to match the data in 2007. xt is then obtained from the human capital index at

timetrelative to 2007. Figure (7) shows the process of risk-free rates on the left panel and

an increase in the fraction of new talented firms entering the economy over the period 1986- 2007. After simulating an economy consisting of 50,000 firms with entry and exit over the period of study, the time series of aggregate manufacturing TFP is obtained.18 _{To compare}

our model’s results with the actual data, Figure (8) presents the transitional dynamics of the model’s aggregate manufacturing TFP along with Chile’s aggregate TFP from Fuentes et al. (2007). Both are expressed as a TFP index, with the TFP of 1986 normalized to 100. The model does a very good job of matching the time path of the Chilean aggregate TFP, which exhibits a gradual increase in TFP once the economy has access to the world technological frontier.

18_{In this transitional dynamics analysis, the distribution of firms in 2007 is not necessarily a stationary}

Real Risk-Free Rate Talent 1985 1990 1995 2000 2005 2010 -5 0 5 10 15 20 25 Year Real Risk Free Rate

1985 1990 1995 2000 2005 2010 0.75 0.8 0.85 0.9 0.95 1 Year Talent

Source: World Development Indicators Source: International Human Development Indicators Figure 7: Two Exogenous Processes: Real Risk-Free Rate and Talent

There are two underlying mechanisms driving this gradual change in the TFP when development is lacking in the financial sector. First, firms need some time to accumulate information in order to overcome financing problems. Because firm types are positively correlated across steps, potential firms have to accumulate information until they get a good pre-lending evaluation for investing in higher-level technology. This might delay the speed of moving up the ladder, as well as the speed of choosing the optimal production level. The time path, therefore, reflects higher-level technology adoption and more efficient resource allocation over time when firm types are more accurately identified through the process of learning and experimenting. Second, the economy waits until the information problem becomes less severe. The fraction of new talented firms entering the economy increases over time, so, from the intermediary’s point of view, firms on average become more talented. Firms born in the latter periods then face fewer financing obstacles. Over time, there will be more talented firms which face fewer obstacles to adopting higher-level technology. This results in a gradual increase in the aggregate manufacturing TFP.

The impact of financial development on the TFP gap has already been shown. Now, it is interesting to see how an improvement in financial development affects the level and speed

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 100 105 110 115 120 125 130 135 140 Year TFP Index (1986=100) Model Manufacturing TFP Actual Aggregate TFP

Figure 8: Transitional Dynamics of TFP

of TFP convergence. Figure (9) illustrates the transitional dynamics of TFP for different levels of financial development. The solid line is the benchmark case with the recovery rate and the accuracy of pre-lending evaluation calibrated for Chile’s economy. Better finan- cial development leads to productivity improvement by stimulating technological progress through technology adoption and by increasing the efficiency of resource allocation. On the one hand, higher recovery rates, either from reducing liquidation process costs or from regulatory reforms, result in a lower cost of information accumulation. An increase in the loan recovery rate from 21% to 91% improves the TFP level by approximately 5% as more firms are allowed to learn their true types. However, the speed of convergence is actually quite slow. Firms still need some time to accumulate information. On the other hand, a more accurate pre-lending evaluation reduces the need for information accumulation and enables high-type firms to move up the technology ladder at a faster pace. Compared to the benchmark case, when the country adopts the U.S. financial practice, the TFP not only converges to a level which is approximately 30% higher, but the speed of convergence is

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 100 110 120 130 140 150 160 170 Year TFP Index (1986=100) Recovery Rate + Pre-lending Evaluation (θUS, ξUS) Pre-lending Evaluation (θUS,ξ) Recovery Rate (θ,ξUS) Becnhmark (θ,ξ)

Figure 9: Transitional Dynamics and Financial Development also doubled.