*2.1. Data*

A series of power crises in Ghana, mainly due to low water inflows, were recorded during multiple periods. The first power crisis dates back to the early 1980s, and this was followed by another in 1998. During these periods, many large-scale electricity users did not operate at their full capacity. Hence, we constructed our time-series data set starting from the year just before the policy enforcement up to the year just before the second power crisis took place in 1998.

Due to power crises, some large-scale electricity users ceased operations either temporarily or permanently. We excluded those SLT users from our data and limited it to the companies that sustained their business during our sample period to construct strongly balanced panel data. Thus, we constructed panel data for 183 SLT companies for five years, namely, from 1994 to 1997 and for 2012, which comprised 915 observations. Our data included power factor values of these SLT companies obtained from the ECG. Data collection took place in 2017.

Table 1 shows the summary statistics for these 183 companies. Our outcome was a dummy variable that indicated whether the firm improved its power factor compared to the previous year; it took a value of one if the firm's power factor improvement from the previous year was strictly positive, and zero otherwise. SLT customers are categorized in terms of the voltage with which their electricity is supplied. High-voltage SLT customers are those firms that are supplied electricity at 33,000 volts; medium-voltage customers are supplied at 11,000 volts; and low-voltage SLT customers are supplied at 415 volts. The observed panel data from the ECG provide information for SLT customers in Greater Accra, which consists of Tema, East and West Accra, as well as the Western Region of Ghana. Tema is the industrial hub of Ghana, and most SLT customers are located in these study areas.

Figure 1 provides a box plot of the power factor distribution over the sample period and clearly shows the overall improvement of the power factor among the SLT customers over the years. The policy was first announced in 1994 and enacted in 1995. Table 1 shows that as many as 88.5% of firms improved their power factor between 1994 and 1995, immediately after the policy announcement. The mean and minimum values of the power factor among these firms continuously improved over the period. By 2012, the average was above the penalty threshold of 90% and the minimum value had reached as high as 74%.


**Table 1.** Summary statistics.

*Notes*: The data includes a balanced five-year panel of 183 firms. The power factor data are provided by Electricity Company of Ghana and measured in the incremental unit of 0.01. Year 1994 is before the policy enforcement and years 1995 to 1997 and 2012 are after policy enforcement. Improvement of power factor is a dummy variable that takes a value of one for the firm whose power factor has strictly improved since the previous year, and zero otherwise.

**Figure 1.** Box plot of power factor distribution over the sample period. A line in the middle of each box indicates the median of the sample in each year. The left and right edges of each box show the first and the third quartiles, respectively. Whiskers show the upper and lower adjacent values. The upper (or lower) adjacent value is the largest (or the smallest) observation that is within 1.5 times the interquartile range from each edge of the box. Dots are the units outside of the adjacent values.

#### *2.2. Identification Strategies*

The summary statistics above seem to indicate the effectiveness of the power factor correction policy introduced by the government of Ghana. However, the unobserved heterogeneity between the efficient and inefficient units may well confound our outcome in terms of whether they improved their power factor when facing the penalty set forth by the policy. That is, we cannot simply compare the outcomes of inefficient firms to those of more efficient firms above the threshold when investigating the impact of the power factor correction policy on the improvement exhibited by these firms.

We bypassed this issue of potential endogeneity by conducting an RDD with a cutoff at the penalty threshold set by the policy. RDD is a quasi-experimental method used to identify the average treatment effect of those units around the threshold called a cutoff (please see Appendix A for more details). In the context of RDD, treatment assignment is performed according to whether the observation units are below or above the cutoff. RDD enables a local average treatment effect (LATE) to be identified for those units around the cutoff, even under a situation like ours where conducting a pure randomized experiment or randomized controlled trial (RCT) is not possible (see, for example, Moscoe et al. [22] for details.) When the treatment assignment is unambiguously determined by whether the unit is above or below the cutoff, it is called the sharp RDD. In our case, units will face a penalty if the power factor is below the threshold but not if the power factor is above or equal, without exceptions. Therefore, we must utilize the sharp RDD strategy. In turn, if the treatment assignment depends, but not solely, on whether the unit lies below or above the cutoff, one must use the fuzzy RDD. That is, if by the research design, noncompliers exist, fuzzy RDD is the appropriate identification strategy.

According to the policy, firms whose power factor is below 90% are charged a penalty. Note that firms cannot independently observe their power factor precisely, which suggests that it would be difficult for firms to precisely manipulate their power factor values. Instead, the power factor is measured periodically by the electricity company. In the case of Ghana, the ECG reports their power factor to the firms along with the amount of the penalty, if any. At the end of each month, ECG delivers the electricity bills along with the amount of penalty and the power factor to the customers. The firm then decides whether to invest in power factor improvement. Our data only contain the annual average of the power factor reported to the customers in our sample. To allow for this time lag in decision making by the firms, we used the power factor in the previous year as a running variable that indicated whether the firm faced the penalty in the previous year. Although the penalty scheme designed by the policy in Ghana exhibits a kink at the threshold because our outcome is a binary variable, we still adopt an ordinary discontinuity design, rather than a kink RDD. Because our outcome variable is an indicator capturing whether the firm has improved its own power factor from the previous year, the same company should be tracked to enable our identification. As mentioned earlier, our outcome was a binary variable that took a value of one if a firm strictly improved its power factor independently from the previous year, and zero otherwise. This empirical strategy with lagged and differenced variables made our working sample a four-year panel from 1995 to 1997 plus 2012 for 183 firms, consisting of 732 observations.

ECG measures the power factor of SLT customers in the incremental unit of 1%. Thus, any firm whose power factor is equal to or less than 89% faces the penalty, while those at 90% or above do not. We, therefore, set the cutoff of the running variable at 89.5% in our RDD to determine whether this policy implemented by Ghana's government indeed induced SLT customers of the ECG to improve their power factor.

#### **3. Results**

Table 2 presents the RDD estimation results. Column (1) shows the impact of the penalty policy, measured as a gap in the power factor improvement probability between those two types of firms, namely, those whose power factor in the previous year was just above and those whose power factor was below the threshold, estimated using the full sample. Column (2) shows the same impact estimated using only the subsample from 1995 to 1997. We refer to them as Models 1 and 2, respectively.

The coefficients were significantly negative in both models, which indicated that, relative to those immediately below the cutoff, those firms whose power factor was immediately above the cutoff in the previous year exhibited a strictly smaller probability of improving their power factor in the current year. In other words, the firms that were penalized were more likely to improve their power factor in the following year.



*Notes*: Standard errors are in parentheses. Statistical significance at 1% is indicated as \*\*\*. The dependent variable is a dummy variable that takes the value of one if a firm strictly improved its power factor since the previous year, and zero otherwise. The running variable is the power factor in the previous year with a cutoff at 0.895. The model in column (1) uses the entire sample of four years, namely, three years from 1995 to 1997 as well as 2012. The model in column (2) uses the subsample of three years from 1995 to 1997 only. Bandwidths in both models are selected by a mean-squared error optimal bandwidth selector. Kernel type of a triangular function is used in both models.

This result is also clearly shown in Figure 2, where the probability of power factor improvement is shown on the vertical axis over the level of the power factor in the previous year on the horizontal axis. Panel (a) shows the figure for Model 1, while panel (b) does the same for Model 2. In both figures, there is a clear discontinuity at the penalty threshold, which is shown as a vertical line. The results show that firms slightly below (i.e., on the left of the cutoff) were much more likely to improve their power factor than firms that were slightly above the threshold line (or on the right of the vertical line). Indeed, the probability of power factor improvement was approximately 90% for firms immediately below the threshold, while only approximately half of the firms immediately above the threshold exhibited an improvement (the gray dot shows the local average within each bin).

A closer look at the result reveals that the effect is stronger in Model 2 than in Model 1. The estimate of the gap in the probability of power factor improvement between firms immediately below and those immediately above the cutoff is as large as 59.8% in Model 2. Figure 2 also shows that the gap is larger in Model 2. The plot of the probability of power factor improvement in Model 2 depicted in panel (b) of Figure 2 shows that firms that were slightly above the threshold were less likely to improve their power factor than the firms in Model 1 depicted in panel (a). In Model 2, we have only three consecutive years; therefore, the resulting greater impact in Model 2 suggests a strong short-term effect of the policy. These results imply that the policy was effective in giving a strong incentive to firms, particularly those that fell slightly below the penalty threshold, to improve their power factor, even in the short term.

**Figure 2.** Probability of power factor improvement and its discontinuity at the penalty threshold. The probability of power factor improvement is on the vertical axis, and the level of the power factor in the previous year is on the horizontal axis. The cutoff is shown as a vertical line at 0.895 of the horizontal axis. The number of observations used in panel (**a**) is 732, of which 454 are on the left and 278 are on the right of the cutoff. The number of observations used in panel (**b**) is 549, of which 366 are on the left and 183 are on the right of the cutoff.

## **4. Concluding Remarks**

In confronting its energy crisis, the government of Ghana enacted a power factor correction policy in 1995. The policy imposes a penalty on large-scale electricity users, labeled as SLT customers of the ECG, when their power factor falls below the threshold of 90%. This paper investigated the policy-induced improvement in these firms' power factor by applying RDD to panel data for 183 SLT customers. Our sample period ranged from 1994, when the policy was first announced, to 1997 and also included data for 2012. Specifically, we defined our running variable as the value of the power factor in the previous year, with the cutoff being the penalty threshold. Our outcome was a binary variable indicating whether the firm strictly improved its power factor since the previous year. The results show that the SLT customers whose power factor fell slightly below the threshold in the previous year were indeed more likely to improve their power factor, and the effect was stronger when we limited our sample period to a shorter term. This finding suggests that the power factor correction policy implemented by Ghana's government had an immediate impact on energy efficiency improvement by the country's large-scale electricity users.

Over the last few decades, the total power generation capacity has been constantly increasing in Ghana, and the majority of such change is attributable to the growth of thermal power generation. As a result, the installed capacity of hydro power is now 1584 megawatts and that of thermal is 3456 megawatts, while renewable energy is only approximately 42 megawatts [23]. With the thermal share of the generation mix now being at 68% and hydro set to reduce further, electricity prices will largely depend on international fuel prices; Ghana will thus be more vulnerable to global energy shocks. Energy efficiency has become even more relevant, and power factor improvement is one of the most important, simplest, and inexpensive strategies for achieving efficiency. For Ghana, like other new emerging economies with low energy efficiency, an efficient and stable electricity supply is a prerequisite for achieving its goal of consolidating its middle-income status via industrialization.

**Author Contributions:** Conceptualization, S.L. and Y.Y.; Methodology, Y.Y.; Software, Y.Y.; Validation, Y.Y. and K.F.; Formal Analysis, Y.Y.; Investigation, Y.Y.; Resources, S.L.; Data Curation, S.L. and B.H.; Writing-Original Draft Preparation, S.L.; Writing-Review & Editing, Y.Y. and K.F..; Visualization, Y.Y.; Supervision, Y.Y.; Project Administration, Y.Y.; Funding Acquisition, Y.Y.

**Funding:** This work is partly supported by the Ministry of Education of Japan Grant-in-Aid for Scientific Research #16K03628.

**Acknowledgments:** We thank Takahiro Ito for his constructive comments.

**Conflicts of Interest:** The authors declare no conflicts of interest.

#### **Appendix A**

*A.1. Regression Discontinuity Design*

Let *Ti* be the treatment variable for firm *i* such that

$$T\_{\vec{i}} = \begin{cases} \ 0\_{\prime} & \text{if } z\_i \ge \overline{z} \\\ 1\_{\prime} & \text{if } z\_i < \overline{z} \end{cases}$$

where *zi* is a running variable for firm *i*, and *z* is the cutoff of the running variable. In our context, *Ti* is an indicator that firm *i* faces the penalty, and *zi* is the power factor of firm *i* in the previous year.

We then describe the outcome *Yi* as

$$Y\_i = \beta\_0 + \alpha T\_i + \sum\_{k=1}^{K} \beta\_k (z\_i - \overline{z})^k + \sum\_{k=1}^{K} \gamma\_k (z\_i - \overline{z})^k T\_i + u\_i$$

where α gives the causal effect of the treatment.

In estimating the causal effect α, we weight observations according to the distance to the cutoff on the domain of the running variable. The weight is computed automatically by optimizing the mean-squared error of the estimation.
