Not Quite Blogging

This is a good time to announce that I am taking a break from writing economics blog posts on this blog for the Fall Term. Instead, I will be featured on Not Quite Noahpinion! Our team profile can be found here, and I already have a post on gold returns up.

But don't worry, this blog won't completely die out. I will be writing more technical pieces for this blog. In particular, I want to write some tutorials on some R functions, as I have accumulated a good bit of experience with them over the summer and I hope to make the beauty of R more accessible to my fellow college researchers.

I encourage you to follow Noah's blog, and as always, you can stay in touch with me through Twitter (@yichuanw). Tune in for more economics come winter!

Quartz: High-speed rail is at the foundation of China’s growth strategy

This is a link and data supplement to my second (solo) Quartz column, which was about China's high speed rail system. The thrust of the column is that, even though high speed rail is oft maligned as an overinvestment, it actually serves many crucial roles to help China both grow in absolute terms and rebalance towards consumption. I feel like this argument will be a gold mine for China infrastructure bulls like Scott, as by digging through some Chinese news articles I found nuggets like this (my translation)

Wan Xiao [the train station manager] explained, at 10 PM on June 25th, after the railway administration released the news on the website that the line would open on July 1st, that evening around 50,000 people called to ask about the train, and over 14,000 messages were left.

(You can check my translation of "万晓介绍，6月25日晚上10点，当铁路局通过官方网站发布汉宜铁路7月1日开通的消息后，当晚的访问量就达到了其上限人数5万人次，留言达到1.4万多条。")

I had a lot of fun reading these Chinese news articles, and I'm sure my parents got a kick out of seeing me finally reading Chinese of my own accord.

There were three points from the column that I wanted to elaborate on.

First, instead of focusing on some kind of Rail/GDP number, I decided to focus instead on Rail Turnover/Length of Rail. I felt that this statistic was more descriptive because it captured the idea of rail intensity, or how much each stretch of rail was being used. In many of these overinvestment narratives, you hear about how there are all these train stations that aren't being used and how it's all just overbuilt. But when you look at the sheer amount of people and cargo that are being moved on the rails, it makes you question whether the problem is excess capacity or actually excess demand.

Second, while I partially addressed ridership concerns in the article, I wanted to go further into the effect of high speed rail on the composition of transportation infrastructure in China. Obviously, if China builds more rail, airlines become less competitive. I see this as an advantage because it allows China's infrastructure to grow in a more environmentally friendly manner. Additionally, better rail infrastructure takes the burden off of highways by moving more passengers onto the faster moving trains. Therefore, by emphasizing the trains, China can take the burden off of the "planes and automobiles" part of its transport strategy.

While this may seem self evident now, there were actually concerns high speed rail would actually worsen the highway situation. In an editorial criticizing Chinese rail, China expert Patrick Chovanec outlined a bear scenario in which the introduction of high speed rail crowds out slow speed passenger rail (which it has). The migrant workers, who then cannot afford to pay for these high speed rail tickets, then opt for bus travel, further crowding the highways.

But given the ridership statistics I pointed out in my article, that just doesn't seem to be the case. Moreover, recent evidence suggests that rail has had the benefit of crowding out auto travel. One example I found was from the Qiangjiang news, which reported that after the opening of the Wuhan-Yichang rail line, demand for bus service from Qianjiang -- a city alongside the high speed rail tracks – to Wuhan fell by nearly 60 to 70%. The Yichang transport station this year also saw its ground transport volume unchanged from one year ago at 45,000 passengers. Given the massive growth in rail, this suggests that the bear case outlined by Mr. Chovanec hasn't come to pass.

Third, while my article focused on the passenger side of rail development, freight rail has also become more intense. In particular, freight intensity in many inland provinces, such as Guangxi, Hunan, and Qinghai has been growing at a steady pace. This bodes well for the development of inland infrastructure, as it means more freight needs to be moved, and high speed rail will help open up the capacity for that to happen.

As always, a link to the data is on the data page. Please reach out if you have any questions.

A Primer On General Equilibrium, or Why Money Matters

This post is meant to be a short summary of how to think about macroeconomics in terms of general equilibrium. During my conversations with Michael Darda this past summer, it became painfully apparent that clients tend to struggle with how to put money and goods markets together. As a result, I thought I should put together a little piece on my basic approach to thinking through these kinds of "across market" effects, and why it matters for some of the policy debates of our day.

Any macroeconomy can be broken down into two main markets: a real market for current goods and services, and a financial market for claims on future goods and services. For brevity, I will reduce the model for financial assets to the market for money, which, because of money's role as a store of value and medium of exchange, captures the notion of "claims on goods". To simplify further, I take all the markets for goods and reduce them down to one composite market, say, for apples. From this caricature, we can start thinking about how markets fit together.

In normal times, people receive apples and money from the sky in the form of endowments (i.e. their wealth), and they make decisions about how to balance their cash and apple balances. Apples are transacted, bellies are filled, and life is good.

But suddenly, a recession hits. What does this look like? By definition, a recession is when there is a general glut of goods that aren't consumed. In this toy economy, this corresponds to a situation in which some people have apples but choose not to eat them! This may seem peculiar, but remember that the market for apples in this model represents a composite of all goods markets. So it could be the case that while everybody has apples, some want Red Delicious while others are looking for the tartness of Granny Smith. In more formal economic models, this is glibly incorporated by requiring that people do not consume their own endowment and instead trade for consumption. In any case, apples aren't eaten and we have a rotten general glut.

But this seems peculiar -- aren't markets supposed to clear? Not necessarily. Prices don't always adjust instantly, so we can have excess supplies and excess demands. However, economists do have a way to constrain what this non-clearing state looks like. In particular, according to Walras' law, assuming everybody spends all of their wealth, if there are excess supplies (i.e. too much produced) in some markets, then they must add up to excess demands (i.e. too little produced) in other markets. In other words, even if supply does not equal demand in each market, supplies must add up to demands across markets.

The requirement that everybody spends their endowment is crucial. It means that Walras' law doesn't apply just to the market for apples because not everybody spends all their wealth on apples. Instead, some people may put their wealth in money. But once we include the money market, we do have the condition that everybody spends their endowment, and therefore Walras' law does apply to the entire macroeconomy of apples and money.

This leads to the most important conclusion from general equilibrium theory as related to monetary economics:

If there is an excess supply of goods, it must be the result of excess demand for money.

The goods market by itself is not enough to generate a recession with a general glut of goods. Only when there is the possibility of excess demand in money markets can recessions actually occur. Therefore the market for money is what gives a macroeconomy its business cycle feel. This is why money is so important for macro -- fluctuations in the money market are the proximate cause for any general fluctuation in the goods market. This is why, as Miles Kimball says, money is the "deep magic" of macro.

While this "apples and money" approach is the canonical presentation of general equilibrium, it is not the unique representation. For another interpretation, think about what the financial market really is. Since it represents the entire universe of claims on future goods, finance can be understood as a veil between the present and the future. So instead of focusing on the relationship between goods and financial markets at one point in time, we can cut out the middle man and instead think of general equilibrium as a sequence of goods markets that occur across multiple points in time. In this version, there is no financial market per se, but buying an apple in "tomorrow's goods market" represents buying a financial contract in the canonical model. Therefore, instead of thinking about the markets for goods and money, we can instead think about the markets for goods today and tomorrow.



The same excess supply and demand relationship works in this model. If there is an excess supply of goods today, then it must mean that there's an excess demand for goods tomorrow. So in this version of the model, the reason apples aren't eaten today is because people want to wait and eat apples tomorrow. So we get a corollary to the above conclusion:

If there is an excess supply of goods today, it must be the result of an excess demand for goods tomorrow.

Each of these stories has its own strength. Since the first goods-money model includes actual money, it can help us understand how the price level is determined through monetary neutrality. On the other hand, since general equilibrium is only concerned about relative prices, and since individual dollars are not transacted in the second story, the second story has no "goods/money" relative price -- i.e. the second story cannot pin down an aggregate price level. However, the second story does a better job of being explicit about intertemporal choice. And for now, this intuition about relative prices between the past and the future will be powerful enough that I will focus on this second approach.

So if recessions are caused by an excess demand for goods tomorrow, how does policy fix a recession? Here, our microeconomic intuition will suffice. If we want to reduce excess demand for a good tomorrow, all we need to do is raise its price relative to today. And since the price of an apple tomorrow is just the amount of money I need to save to afford it tomorrow, lowering the rate of interest between today and tomorrow is sufficient to raise the relative price of tomorrow's apple and get me to consume today. Note that this has an analogue in the first "goods/money" story. By lowering the interest rate on financial assets (and expanding the supply of money), this makes financial assets less worthwhile to hold. People then pivot away towards the goods market, and the general glut is consumed.

If recessions are generated by this process, the interest rate story shows why monetary policy can be politically difficult. Monetary policy, in this model, just tries to change the relative price of consumption today and tomorrow to resolve the general glut. But just when people most want to save, the interest rate falls and it becomes more expensive to do so! This is part of the more general political difficulty of the price system. Under a price system, the most desired objects are the most expensive. While this may be unpleasant, it's certainly efficient and necessary for avoiding recessions.

Now, one question that arises is why the real rate of interest doesn't automatically equilibrate to solve these excess demand problems. This is actually a very good question, and is the reason why monetary economics is so important. The primary explanation is that the Federal Reserve may not move fast enough to provide enough money to serve as claims on tomorrow's goods, and therefor the real rate spikes when a crisis hits. This is why we invest so many resources into studying monetary economics, because it is the proximate cause of most recessions.

So here we close the loop. From a relatively simple model, we now have a theory of employment (apple recession), interest (relative prices), and money (in the canonical representation).

Now we get to the fun part -- applying this framework to some of the policy debates of the day.

Let's start with monetary policy. By visualizing a macroeconomy through a sequence of markets, it becomes apparent why forward guidance matters. Even if the interest rate for today is zero, future interest rates may not be. Therefore, by promising to hold rates low for an extended period of time, that makes future apples more expensive relative to current apples. Now, the exact adjustment path may not be ideal, but so as long as we lower the interest rate enough to create enough excess supply in the future, we will be able to restore demand today.

Interestingly enough, quantitative easing is not in this picture. However, that's a long conversation that will receive its own post in the future.

We can also think about fiscal policy in this framework. If a recession is just a sign that there's excess demand for goods tomorrow, then for fiscal policy to work, it must convince people to bring some of their future consumption into the present. The conventional old-Keynesian approach to this (i.e. the Intro macro approach), is to argue that by giving people more money today, that makes them want to consume more today, which then directly solves the recession. But the actual mechanism is more subtle, and the efficacy of fiscal policy is entirely determined by its effect on intertemporal choice.

The Ricardian critique of fiscal policy also pops out of this framework. Ricardian equivalence, roughly speaking, argues that since consumers will take the future costs of taxation into account, therefore fiscal policy will have little effect. In this model, this future cost of taxation means people don't reduce their excess demand for goods tomorrow. Because they know the government will take away those apples, the agents are trying to save up so as to have enough to eat when tomorrow comes. Therefore the whole Ricardian effects/positive multiplier debate again just comes down to whether fiscal policy is actually effective at changing the patterns of consuming today and tomorrow.

In this context, the Federal Lines of Credit proposal from Miles Kimball makes a lot of sense. By extending lines of credit to those people who need it most, Federal Lines of Credit can persuade people to reduce their demand for goods tomorrow in favor of goods today.

I'm not entirely satisfied with this model. In particular there are the glaring omissions of rigorous foundations for inflation or intertemporal production. However, I do think it does serve as a baseline for understanding why intertemporal choice is so important for understanding macro, and I hope to expand on it in future posts.

Pictures were drawn in Paper 53.

A Practitioner's Thoughts on Market Monetarism

This summer, I have been working at MKM partners with Michael Darda doing a wide range of macro research. Since Michael is one of the leading street economists who uses a lot of market monetarist concepts in his work (monetary offset, nominal GDP targeting, market signals), I have accordingly been doing a lot of work on monetary policy and nominal GDP during my time here. This blog post is meant to talk about some problems I have encountered as I have tried to write about these market monetarist concepts in my reports for Michael, and I hope this can be useful for fellow market monetarists -- especially fellow practitioners.

Before I delve into the specific problems, it might be useful to consider a summary of key propositions that recur in market monetarist discussions. In no particular order, they are summarized below:

1. Interest rates are an unreliable indicator of the stance of monetary policy. As Milton Friedman reminds us, low interest rates typically indicate that monetary policy has been too tight, and high interest rates typically indicate that monetary policy has been too easy. For example, monetary policy throughout Japan's lost decade was too tight as the central bank would raise interest rates at the first sign of inflation. But as a result, Japanese interest rates have held steady at very low levels. On the other hand, monetary policy in the United States during the 1970's was far too easy, and as a result interest rates were very high. This is because the level of the 10 year nominal rate is determined more by money velocity than anything else.

2. The only reliable indicator of the stance of monetary policy is a nominal aggregate, such as nominal GDP. Given that interest rates are an unreliable guide, we are left with judging a policy stance by its outcomes. Since the goal of monetary policy is to provide a nominal anchor, then the stance of monetary policy is determined by how the nominal aggregate performs relative to the target. So if nominal GDP is above trend, monetary policy is too tight, and if it is above trend, then policy is too easy. 

3. Market signals serve as the optimal forecast of future economic conditions. Since the price of securities typically reflect all available information, they can serve as a high frequency measure of market expectations. This is particularly attractive because it means a relatively small firm like MKM can abstract away from building a structural forecasting model and instead focus on interpreting the price signals in individual markets. 

4. Never reason from a price change. Clients struggle with this one, but it's really quite simple. In economics, whenever there's a change in conditions, it's because a curve -- supply or demand, liquidity preference, etc. -- has shifted. As a result, a quantity or price changes. But for any given increase in price, whether quantity goes up or down depends crucially on whether the change in price is caused by a supply or demand shock. This sounds like trivial microeconomics, but people often forget it when they start talking about finance. Clients tend to go straight to questions such as "how does this rate hike affect housing markets?" or "how will this increase in crude prices affect the economy?" without asking "why are rates rising?"
Looking back at some of the work I did this summer, I have two takeaways -- one positive, one negative -- from these four core ideas.

First, the positive. The notion of market signals and of reasoning from curve shifts (i.e. 3 + 4), and not price changes, led me down an interesting path of trying to identify curve shifts from financial market data. This led to my "Market Monetarist Approach to the Interest Rate Puzzle". The core idea here is that you can use three financial indicators -- the SP500, the TIPS spread, and the 10 year treasury -- as proxies for three "real" economy indicators -- nominal GDP, the inflation rate, and the risk free rate. Now, the stock market one is a bit difficult because equity values are not only a positive function of cash flows (~ nominal GDP), but also a negative function of the risk free rate (because of discounting). Nonetheless, it's one of the few real time metrics we have for growth expectations.

With these three changes, I interpreted the recent change in the relationship between the 10 year inflation breakeven and the SP500 as a sign of an aggregate supply shock. This was my conclusion from some time series analysis that showed the slope of the relationship between the SP500 and the TIPS spread has not changed, but the intercept has increased. Statistically, this translates to the statement "at all levels of expected inflation, the stock market has higher returns." If we accept the above dictionary into real economy terms, this translates to "at all levels of inflation, nominal GDP is higher" -- the smoking gun of a supply shock.

I did some follow up work on interpreting these structural shifts in the interest rate puzzle post.

But now, the negative. Identifying the stance of monetary policy by the outcome leads to circular statistics. If you attribute all fluctuations in nominal GDP to bad monetary policy, then of course monetary policy will seem like a big issue! Put another way, you can observe the positive relationship between nominal GDP and real growth without requiring that monetary policy drives nominal GDP. The tight correlation between nominal GDP and a whole host of other aggregates does not identify a market monetarist viewpoint of the world. And because of the Lucas critique, monetary policy may be unable to exploit this relationship to restore real growth. Perhaps if you use a good bit of economic history, you could identify certain scenarios of exogenous monetary contractions. But in the end, focusing on nominal GDP to determine the stance of monetary policy makes it hard to do any kind of systematic statistical analysis.

But that doesn't mean there isn't any statistical evidence.

In my view, one of the more robust pieces of evidence for the power of monetary policy comes from an analysis of fiscal multipliers in open and closed economies. To see why this matters, we need to think about Mundell's impossible trinity. The impossible trinity states that no economy can simultaneously have free flows of capital, a pegged exchange rate, and a sovereign monetary policy at the same time -- you have to give up at least one. Given that most countries have been dismantling their capital controls (especially since capital controls eventually become porous), you can identify whether a country has a sovereign monetary policy by seeing if it has a pegged exchange rate regime. Econometrically, the exchange rate regime serves as an instrument for effective monetary policy that avoids the problems inherent in using interest rates.

With a few more assumptions, we'll be going places. Suppose that central banks with sovereign monetary policies tend to maintain some kind of nominal stability -- whether inflation or nominal GDP. Then as a result, these central banks would tend to offset fiscal policies more, as those central banks under pegged exchange rates would have to subjugate their monetary policy to maintaining the exchange rate. As a result, if monetary policy matters for real growth, then countries with pegged exchange rates (and therefore no sovereign monetary policy) should exhibit higher fiscal multipliers. This is because these countries have no potential for fiscal offset. By this chain of logic through Mundell's policy trilemma, I have reduced the problem of "Does monetary policy matter for real growth?" to "Are fiscal policy multipliers higher in pegged exchange rate regimes?"

And are they? Most certainly. In an NBER working paper titled "How Big (Small?) are Fiscal Multipliers?", the authors find that the long run multiplier for countries under pegged exchange rates is around 1.4, whereas the multiplier for countries under floating exchange rates is statistically no different from 0. In fact, the authors themselves come to this conclusion about monetary policy. In particular, they show that the monetary offset if floating rate regimes doesn't come through the current account, but rather through private consumption. Their conclusion is that "consumption responds positively to government consumption shocks only when the central bank accommodates the fiscal shock" -- a sure sign that monetary policy is an important force governing the nominal (and real) economies in the short run.

This pegged/floating exchange rate example bears itself out through the natural experiment comparing austerity in the Eurozone and the United States. Because Eurozone monetary policy has been much more tepid, they can be identified as lacking a responsive monetary policy. So although both economic areas have undergone savage austerity, only the Eurozone has really suffered -- more evidence that monetary policy really does matter.

(Note, an older version of the plot with government spending was used, but data concerns were raised by Mark Sadowski and David Beckworth. In particular, Beckworth pointed out the correct measure of austerity is the change in the cyclically adjusted primary balance, as provided by the IMF Fiscal Monitor)

However, one consequence of this kind of analysis is that it's hard to quantify the effect of monetary policy on nominal GDP growth -- there's little guidance on how much QE translates into how much growth. Perhaps the expectations channel means that this effect is impossible (and maybe even meaningless) to quantify, but it is a limitation of this mode of analysis.

Once we accept this analysis and think of monetary policy as driving nominal growth, then the market monetarist mindset of using deviations of nominal GDP to track monetary policy starts to make sense. Once you establish the empirics through other means, the theory of market monetarism comes into play.

Overall, I find the core ideas espoused by Scott Sumner and fellow market monetarists very powerful. In some regards, they lend themselves easily to financial econometrics and help to organize a a coherent explanation of the macro environment. But some of these ideas need more formal empirical backing -- something that becomes very apparent when talking to clients.

China's Growth: A Look Inland - Data Supplement

Today my Quartz column on the changing economic geography of China was published. In this post I intend to cover some extensions of the article that did not make the cut, and in addition go through some of my data analysis procedures so as to provide a resource for fellow students doing similar research.

A central idea is that the base unit of analysis for the Chinese economy should be the province. This is because China's massive size make its provinces as large as entire countries. For example, Guangdong, a coastal province, has 108 million residents. In comparison, Mexico only has 112 million residents and the entire Western United States only has 71 million residents. The entire continent of Europe has only around 740 million people -- a little less than half that of China's 1.3 billion. As such, lumping all the Chinese provinces together into one entity called "China" papers over so much heterogeneity in income levels and growth rates -- resulting in a very misleading picture about the actual economic situation.

To get an idea of these massive income differences and why it's important to look at provincial data, consider the stories of Guangdong and Guangxi, two neighboring provinces in southern China. In 2011, Guangdong, the relatively rich coastal manufacturing center, had per capita income of about 51,000 yuan (~$8,300 USD). Yet Guangxi, an inland province right next door, had nominal per capita income of only 25,200 yuan (~$4,100). Does it really seem plausible that Chinese growth will slow down so suddenly  that two neighboring provinces whose names differ by one Chinese character* will maintain such a large income gap into perpetuity? Given that Guangxi's per capita income increased by a factor of 3.36 from 2001 to 2011 and Guangdong's per capita income only increased by a  factor of 2.06, I would have to say no. Moreover, even if income levels do not completely converge, income growth should. Since Guangxi's income growth rate is still so high, I have to conclude that it's growth will likely be sustained for some time. Had I not analyzed the provincial data, I would have instead seen a downward trend in national real GDP growth numbers and concluded that China will suddenly slow down. But by taking into account the way growth rates evolve across provinces, I arrive at a more optimistic GDP number.

Geography is especially important given that many of the arguments made by Krugman and a recent IMF working paper center on Chinese labor markets. The argument is that since China has become richer, China has reached "peak peasant" and can no longer sustain such high levels of growth. But I'm left asking -- which provinces have hit this peak? Given that the inland provinces are still relatively poor, there still seems to be a lot of room for these provinces to grow. Although the move towards manufacturing in inland provinces may be a sign that coastal provinces are facing labor shortages, the "reach for peasants" suggests that inland China still has plenty of labor market slack left As a result, I am left quite skeptical about these dramatic bear stories for a sudden slowdown the Chinese economy.

I also want to add one more graphic to this conversation about China's growth. While the scatterplot in the column does a good job of showing convergence, I wanted another plot to just show how much individual Chinese provinces have grown in the 10 years spanning 2001 to 2011. I settled on the chart below. Besides the components in the legend, the small numbers to the left and right of each dot is the nominal per capita income (in thousands) for the specified province and year. The black number in the middle of the band is then the ratio between 2011 and 2001 levels of real GDP.

The nominal number is useful because it allows relatively quick conversions into U.S. dollars. As such, it seems that the per capita income in Shanghai is around $13,300 -- a level slightly ahead of Mexico's per capita income of $10,247 and the U.S. poverty line for a single person household of $11,344. The black multiple then emphasizes how much individual Chinese provinces have grown. These above-three multiples correspond to over 12% growth, so if a child entered elementary school in 2001, then by the time he or she goes into elementary school, GDP in that province would have doubled.

Of course, there are risks to the bull case that I present in my Quartz column.

Chief among these risks is if there's an environmental constraint prevents the inland provinces from obtaining the same levels of income as the coastal provinces. The Solow model (on which convergence is based) does not take into account natural resources, so if natural resources run out this process of convergence could fall apart. This does not have to be a hard scientific constraint either -- public outcry against environmental destruction would have a similar effect. While I agree that China does face serious environmental challenges (particularly in air and water pollution), I don't think protests will play as large of a role that people suggest. Remember that the recent large scale environmental protests -- in Zhejiang against a petrochemical plant and in Guangdong against a nuclear plant -- have taken place in the richer coast. Therefore inland China still has a way to go before this environmental constraint becomes more severe.

Others may raise the issue that the Chinese provincial data are a dangerous form of "science fiction". Indeed, it is a bit peculiar as the sum of all the provincial GDP numbers does not equal the total national GDP. But as Princeton professor Gregory Chow notes, while year to year GDP growth rates may be easy to manipulate, levels are not. Since the levels are recollected every year, measurement errors accumulate and therefore any kind of fake data becomes unsustainable. As a result, I focused on a 10 year average growth rate to resolve the issue of year to year measurement errors. Moreover, a recent San Francisco Fed economic letter found that national Chinese data seems to be accurate and consistent with a wide variety of indicators. Thus it seems doubtful that the main convergence result was just the result of data manipulation.

The bottom line is that China's great size means that attention needs to be paid to the individual provinces. On the basis of the provincial levels of growth, I am left quite optimistic about the future of Chinese growth.

If you want to try and replicate it (please do), just consult the public dropbox folder. The workflow goes from running all the STATA do files first and then transitioning into solowQz.R file to draw all the pictures. I have also included a Makefile to go through this workflow. (A Makefile executes all the code in order according to the dependencies. If you plan on doing any major work with code you really should learn a little bit on how to use them)

The one interesting methodological issue was how I used convergence to forecast future provincial growth. What I did was run a weighted least squares regression of average growth rate against initial log income, in which data was weighted by population and the estimator minimized the sum of weighted square residuals. On the basis of this regression, I assumed that the same relationship between initial income and growth continued into the next ten years and constructed measures of what growth should look like. After I had per capita income estimates, I assumed that population in each province would stay, and on this basis calculated total real GDP numbers by adding up the GDP in each province.

I had a fun time drawing the maps as well. I used R to interface with the GADM databases, and you can look at the code in chinaMap.R to get a better idea of what's going on.

If there are any more questions on code, please reach out. My email can be found on my About Me page.

*Guangxi and Guangdong literally translate to the western and eastern expanses, respectively. They are really are two sides of a lingual coin.