"Micro"-economics of minimum wage laws

    I have written a post on minimum wage law and unemployment, stating that unemployment was not obviously increased whenever the minimum wage was raised in Hong Kong. The post intends to explain one idea: other things being equal. If other things are not equal when you assess the impact of a policy, you have to find a way (such as statistical method) to control these other things first, or your assessments are simply invalid. 
   In this post, I want to discuss another blind spot involved in these analyses, minimum wage law or the like, frequently adopted in high-school economics education. The unemployment implication is drawn by referring to a demand-supply diagram. There is, perhaps, nothing wrong. The danger is that the demand and supply curves are drawn for one labour market as if there is only one type of labour service involved in the market. Of course, we know that in the real world labour services are of various types. The services offered by a barber are greatly different from that offered by a chef. Hence, one demand-supply diagram of aggregate labour service obviously over-simplifies the issue at hand. 

   How will the employment analysis be affected if labour services are broken down into different types when one single minimum wage law is introduced? 

   First, of course, we should consider different markets for different types of labour services. In each market, a different demand-supply diagram should be drawn. 

   Second, when this is done, it is obvious that we will find only some types of labour services are affected while some will not. Unskilled workers with low wages are affected. Skilled workers with high wages will not. Unemployment, if any, should be generated only in the affected sectors. In the situation of Hong Kong, before the introduction of minimum wage law (in 2011), the government had identified two industries, cleaning and security guards, as potentially the sectors that require wage protection and would be affected. 

   Third, this is not the end of the story, however. And this is exactly where multi-sector analysis can offer extra insights. Sectors are inter-related. If one sector is directly affected by the minimum wage, another sector will be indirectly affected, not because the wage of this sector is below the legal requirement, but because this sector will be affected by the affected sector. For example, a worker may work as a salesperson or a security guard. Salesperson's salary is above the minimum wage, and so this sector is not directly affected. However, a salesperson may change job, becoming a security guard as the salary of the latter is improved by the law while other working conditions, such as job stability, work intensities etc, are perhaps better. These inter-sector effects are probably the more pronounced impact of the minimum wage law. 

   In fact, casual observation confirms this. In Hong Kong, security guard for residential properties is one of the most affected sector by the law. Before the law, wages were too low for this sector and most workers were old male retirees. Now, much more different types of people are willing to work in this sector. A very clear change is that female security guards are no longer an exception. Younger guards are also occasionally found. 

   Is there (more) unemployment in this sector due to the law? If we use a simple and single demand-supply diagram for analysis, the answer should be positive. But don't forget that we have many demand-supply diagrams for many sectors. A salesperson is still an employed salesperson before he or she can change job to become a security guard. They don't first quit the jobs and then wait for the security guard industry to employ them, and so in the meantime they are unemployed. What happens may only be the potential supply of security guards is higher than demand, but these excess supply is reflected in many people waiting for job offers from this sector (security guard) while they are currently employed in a less ideal sector (salesperson). Another new source of worker supply may be the household wives. They may not consider working in the past as jobs that they can work may not offer a wage high enough. But they may now consider working. Nonetheless, they may not be counted in the labour force before they find a job (they will not register themselves as job seekers when they are household wives) and they are not counted as unemployed (they work as household wives). Hence, overall increase in unemployment rate may not be observed. But there could be misallocation of labour resource: workers and jobs may not be best matched. 

   Meanwhile, the indirectly affected sector, say salesperson, may have a pressure to raise the wage (though the original wage is already above the minimum wage level). They may not immediately find a job as security guards because the job offers are not sufficient. But their bosses may notice that the outside opportunities for their salespersons are wider. The employors may feel a pressure to increase salary or they may lose workers in an unwanted way. 

   Finally, another industry supposedly significantly affected by the law is cleaning. I am not so sure what have been happening to cleaning workers' situation after the law. I can easily observe employment situation for security guards at residential properties but not also clearly about cleaning workers' situation. My casual observation is that there is not much change in cleaning workers' situation (but if I am wrong, let me know). The sector is still dominated by older female workers. If this is true, why? I think this is due to the sectorial characteristics. Perhaps cleaning is a low-skill job but it is also a very unpleasant job. In a sense, unpleasant job is similar to skilled job. A hurdle has to be overcome before you can work in these industries, and not every one can overcome the hurdle. True, money matters. When salary is increased to a sufficiently high level, more people will try and overcome the hurdle. But does minimum wage law increase wage to the required level as to change people's perception for cleaning job? I think you must have your own answer in mind.  

   As mentioned above, simple analysis of demand and supply in high-school economics has a blind spot. The point is not that demand-supply model is insufficient for analyzing things that happen in the real world. The point is that only one demand-supply diagram is drawn, ignoring inter-sector effects, or different demand-supply diagrams should be drawn to show how one diagram is affecting another. In economics, this is about partial equilibrium versus general equilibrium analysis. Simple economics concentrates almost exclusively on partial equilibrium analysis. But, as shown in this post, general equilibrium perspective is often important. 

Minimum wage law and unemployment

   Minimum wage law has been adopted in most advanced economies for a very long period of time. However, to Hong Kong people, this is a relatively new issue. We adopt it only since May 2011. Before it was introduced, there was a very hot debate especially in related to its impact on unemployment.
   Even high-school economics students know that minimum wage law will generate unemployment as this is a very useful way to introduce one key concept in economics: equilibrium (versus disequilibrium). The introduction of minimum wage law prevents prices from freely adjusting to achieve equilibrium in a demand-supply diagram. The result is that quantity supplied of labour is higher than the quantity demanded of labour and so unemployment is produced. This is the textbook treatment of minimum wage law and has been used for many many years. Beyond textbooks, there are some dissenting opinions (notably the findings due to a 1993 paper by Card and Krueger) but perhaps there are still more professional economists believing in the textbook case.
   This post is not concerned with the academic debates mentioned above. Let's consider if the textbook case of minimum wage law is correct. Then, look at the figures. We can find little evidence, if any, for the hypothesis that minimum wages are to increase unemployment in Hong Kong.

	2010	2011	2012	2013	2014	2015	2016	2017
Hong Kong unemployment rate (%)	4.3	3.4	3.3	3.4	3.3	3.3	3.4	3.1
minimum hourly wage	0	28	28	28-30	30	30-32.5	32.5	32.5

   The most dramatic counter-evidence is that unemployment rate decreased from 2010 (when minimum wage was not effective) to 2011 (when it became effective). The drop is so sharp: from 4.3% to 3.4%. Next, since May 2013, the minimum wage raise from $28 to $30. But unemployment actually fell from 2013 to 2014. Then, since May 2015, the minimum wage raise from $30 to $32.5. This time, unemployment rate slightly went up from 3.3% to 3.4%. Taken as whole, how can we say minimum wage law bring about unemployment? The data is simply not supportive to this hypothesis.

   In fact, around 2010 and 2011, when minimum wage law was first introduced and so this was a hot topic in the society, I often asked students during interview: The data of unemployment rate is not consistent with the prediction by economics. Does it mean the economic theory is wrong? Notice that this was a question given to high-school students. Thus, what I asked for is an answer made based on high-school level economics. But most students did not know how to cope with such a question. Perhaps they was accustomed to learning what has been taught but not to thinking upon what has been taught. Some students, being not able to explain the inconsistency between data and theory, simply replied: perhaps the theory is wrong. But that's also not my expected answer. I didn't try to criticize the conventional theory during interviews (it would be unfair to require students to think beyond the conventional theory but it is fair to require them to truly understand the conventional theory they learn). 

   The answer should be so simple, and is exactly what is the topic of my last post: ceteris paribus or other things being equal. Even if the theory of minimum wage law is correct, it is correct only when other things being equal. If the demand and supply curves do not shift, but the minimum wage is imposed, then unemployment is created. However, if demand curve shifts (say, the economy grows strongly so as to increase labour demand) or supply curve shifts, there need not be (extra) unemployment to be created by the law. We have to know what happen during 2010-2011, 2013-14 and 2015-16 when the wages were increased. Perhaps the economies were good (or bad) at that time. We can never jump to the conclusion that the theory is wrong. Thus, what we need is a model to take account of those relevant factors that affect unemployment rate, such as GDP, labour force change, etc. Only when we control these other factors (by an econometric or a statistical model), we can then assess if minimum wage has extra effect on unemployment. If we have already controlled these other (relevant) factors, and we still find that unemployment rate is not increased, then we can conclude that the minimum wages do not matter. 

Misunderstand "other things being equal"

   In the past summer, I have interviewed many high-school students wanting to study economics in university. As I mentioned in my earlier post, interviews is a useful source for me to know what students have learned in economics.
   In one case, a student (a pretty good one) gave us (I and another interviewer) a question: In economics, a usual assumption made is "ceteris paribus" or "other things being equal". However, in the real world, other things are always not equal, Then, how can we apply the economic theory for analyzing the real world? The theory may never be useful.
   I guess that not only this student but also many laymen may have the same feeling about this assumption used in economics. However, most doubts cast on this assumption is due to a misunderstanding. There is a need to clear up these doubts and remove the misunderstanding if we want to properly learn economics.
   At that time, I gave another answer to thus student. Upon reflection, there is an easier way and more constructive way to answer this student so that he can understand why his suspicion involves a misinterpretation of the "other things equal" assumption. Hence, let me answer his question (again) here.
   For example, when income increases, economic theory (demand and supply) will say that, other things being equal, the demand curve for a normal good will shift rightwards while the supply curve is unchanged. So, both the price and the quantity traded of the good will go up. However, other things are always not equal. But does it mean our analysis is not useful? Certainly not. If we know what "other things" change when income increases, then the economic analysis should simply take also this into account. For instance, if we also know that the cost of production decreases when income increases, then the theory tells us that supply curve will shift down when demand curve shift rightwards. The result: quantity traded certainly increases although price may go up or down. If we want to know whether the price will go up or down, then we have to know some more about the facts: the income increases by how much and the cost goes down by how much and what is the income elasticity of demand and cost elasticity of supply.
   Hence, you can see: The theory is useful. It can predict what happen even if "other things are not equal". But the more complex the event is about (only income increases or cost also changes), the more information (income and cost elasticities) we need for an analysis.
   So, "other things being equal" does not really prevent us from using the theory to analyze the real world. But then you may wonder: if so, why "other things being equal" is assumed? It seems that the assumption of "other things being equal" has not been satisfied and adopted in the case of "income increases while cost also goes down".
   The situation is: the assumption has really been used in the analysis above. When a demand curve shifts, say, from D1 to D2, other things are assumed to be equal. Only income increases and so the demand curve shifts to the right. When a supply curve shifts, say, from S1 to S2, other things are assumed to be equal. Only cost goes down and so the supply curve shifts down. Well, when both things (income increases and cost goes down) happen, wouldn't it be wrong to say "other things being equal"? No. You have to understand that a conducive approach to analyze anything is to analyze things step by step, instead of messing up everything together. To make step-by-step analysis possible, in each step, you had better consider only one thing to change (or you may mess too many things up). So, when you want to know what happens to the demand side, consider only demand factor (income). Other things (cost) are assumed equal. When you move on to the next step - the supply side, consider only supply factor (cost). Now the income has been considered to have increased to the new level already and no longer change further. Other things (income) are equal.
   From this example, you can see that "other things being equal" should not be misinterpreted as really assuming everything else unchanged in the real world. It is, however, necessary for analysis in steps, not messing things up.
   Well, you may still find this interpretation not convincing enough. You may say: when income increases, if other demand factors are also not constant, the demand curve may not shift to the right. Thus, we need to assume unrealistically that other demand factors are equal when predicting a rightward shift in demand curve. But this does not affect my interpretation above: "other things being equal" is assumed for any step-by-step analysis.
   In economics, we often express demand as an equation like this:
Quantity = 100 + 0.8(average personal income) - 1.2(price of the good) + 0.2(price of substitutes) - 0.15(price of complements) + 0.06(other factors)
   Demand equation can be estimated when economists got sufficient data about consumers' choices under different prices, income levels, etc. The above suspicion is like saying that we cannot be sure the demand curve shifts to the right when income increases by 1 unit as price of substitute may fall by more than 4 units at the same time (other things not equal), offsetting the effects from income.
   There are two responses to this suspicion: First, when we say the demand curve shifts rightwards, we have to make sure the income effect will not be offset by "other things" such as price reduction of substitutes. But it is still true that if "other things being equal", income will shift demand to the right. In fact, the parameter 0.8 for income effect says exactly that if "other things are equal", 1 unit increase in income increases quantity demanded by 0.8. It is meaningless to talk about 0.8 if "other things are not equal". If we do not have the parameter 0.8, we cannot even tell that when income increases by 1 unit while the price of substitute reduces by 4 units ("other things not equal") demand will be unchanged. Meanwhile, if we do not know what happen when "other things are equal" (0.8 parameter), we cannot know what happen when "other things are not equal" (both income and price of substitute change). There is nothing paradoxical involved. As mentioned, "other things being equal" is simply an assumption adopted to facilitate the step-by-step analysis. If we cannot divide things in steps and know in each step what would happen (know what would happen "when other things are equal"), we also cannot know what would happen when all steps are taken.
   Second, perhaps someone may concentrate on the last item in the demand equation above. There are always other things other than the factors identified as price of substitutes/complement, and so on, in a model (of demand in this case). In fact, when someone criticize the "other things being equal" assumption, I suspect that most of them have exactly this type of criticism in mind. They may think: there are so many factors in the real world and so how can we not miss some factors? But this problem is not unique to economics. For example, when scientists predict the weather of tomorrow, there must always be some factors other than those that have been identified in their weather model. That's one reason why scientific predictions may sometimes fail. Scientists can only try their best in identifying as many relevant factors as possible. There is nothing wrong and special about this. Of course, social scientists, economists in particular, may find their task of this identifying jobs particularly difficult as society/economy is a complex thing. As scientists, or economists, or even economics students, one should not therefore blame the theory, saying that "other things being  equal" prevents them from doing a good job. If we haven't tried to identify as many relevant factors as possible, it is our fault, not the theory.